Tools

Component Properties	PPM per °C PPM Deviation Temperature Coefficient Capacitor Code ↔ Value Zener Diode Zener Diode Shunt Reg. Resistor Colour ↔ Value Resistor Colour to value LED Resistor
Device Properties	Multimeter Uncertainty
Passive Circuits	RC Charge/Discharge LC Resonant Frequency RLC Impedance ser. RLC Impedance ser./par. Reactance (Xc, Xl) I Reactance (Xc, Xl) II Q Factor Parallel Resistors Voltage Divider RC Filter 1st Order RC Filter 1st Order II RC Filter 1st-4th Order
Power, Energy & Regulators	Power Dissipation DC PSU Efficiency Battery Life Estimator Joule ↔ Watt-hour Energy in a Capacitor Energy in an Inductor Rectifier Ripple PSU Ripple (with DC) Volt Drop wire/cable SMPS Duty & Ripple V.Reg Cap. Designer LM317 Regulator LM337 Regulator
Amplifiers	Op-Amp (inverting) Op-Amp (inverting) II Op-Amp (non-inverting) Op-Amp (non-inverting) II
Frequency, Timing & Waves	Time / Frequency 555 Timer 555 Timer II Duty Cycle ↔ On/Off T. Wavelength ↔ Freq. Quarter-Wave Resonator Transmission Line Z₀
Measurement & Conversion	dB Conversions dBm ↔ mW / W Signal-to-Noise Ratio Decimal ↔ Scientific SI Units ↔ Scientific mm ↔ mils Rectangular ↔ Polar LED Matrix Font Gen.
Material & Field Effects	Current Density Skin Depth Wire Resistance
Fundemental Laws	Ohm’s Law (V=IR) Joule’s Law (P=I²R) Kirchhoff's Law (KCL + KVL) Lenz’s Law Faraday’s Law Coulomb’s Law Gauss’s Law Ampère's Law Biot-Savart Law

Inverting Op-Amp Amplifier

Input Resistor

Rin:

Feedback Resistor

Rf:

Input Voltage

V

Vout: — | Gain: —

Vout vs Vin

Ideal Op-Amp Model:
Gain = - Rf / Rin
Vout = Gain ⋅ Vin
Note: Real op-amps have bandwidth limits, offsets, and saturation; this shows ideal linear inversion.

Zener Diode Shunt Regulator

Component Values

Vz:

Rs:

Load

Rl:

Input Voltage

V

Calculated Output

Vout —

Iz —

il —

PRs —

Pz —

Vout vs Vin

Ideal Zener Model:
If Vin ≤ Vz or (Vin > Vz and (Vin - Vz)/Rs < Vz/Rl): Vout = Vin ⋅ Rl / (Rs + Rl)
Else: Vout = Vz, Iz = (Vin - Vz)/Rs - Vz/Rl ≥ 0

Operating Notes:
Regulation occurs when the current available through Rs is greater than the load current, allowing the zener to conduct.
If Iz falls to 0 mA, the circuit is no longer regulating and Vout behaves like a simple resistor divider.
In Resistor mode the load is represented by Rl. In Current mode the load is represented by a fixed load current.

Practical Design Notes:
Choose Rs so that at the lowest intended Vin and highest load current, the zener still has some current remaining.
Check that Pz is below the zener power rating and PRs is below the resistor wattage rating.
This is an ideal model: it does not include knee softness, dynamic resistance, source resistance, tolerance, or temperature effects.

LED Matrix Font / Pattern Generator (Reversible)

Binary (rows)

Hex (C array)

RC Filter 1st–4th Order, Butterworth

Mode

Order

Selected: 2-order

Resistors & Capacitors (per section)

R:

C:

Frequency Test

Hz

f_c (per section): — | |H(f)|: — | Phase: —

|H(f)| (dB) Phase (°)

Formulas (ideal Butterworth Nth-order):
Cutoff per section: f_c = 1 / (2πRC)
Low-pass: |H| = 1 / √(1 + (f/f_c)^2N), φ = −N·atan(f/f_c)
High-pass: |H| = (f/f_c)^N / √(1 + (f/f_c)^2N), φ = N·(atan(f/f_c) − 90°)

Note: Actual equal-section passive cascades may differ, this just illustrates the sharper knee when using an increasing filter order.

Rectangular ↔ Polar (Complex Numbers)

Quick Overview

Convert a complex number between rectangular form a + jb and polar form r ∠ θ. Type values in either panel and results update automatically.

Rect → Polar: r = √(a²+b²), θ = atan2(b,a)
Polar → Rect: a = r·cos(θ), b = r·sin(θ)
Angle can be shown in degrees or radians. Use DPs for rounding.

Rectangular (a + jb)

a (Real):

b (Imag):

Polar (r ∠ θ)

r (Magnitude):

θ (Angle):

Angle units:

Outputs

Rect:

—

Polar:

—

DPs:

Auto-updating

Notes: θ uses atan2(b,a), so it is correct for all quadrants. Magnitude uses √(a²+b²).

RC Filter 1st Order

Mode

Resistor & Capacitor

R:

C:

Frequency Response

Hz

f_c: — | |H(f)|: — | Phase: —

|H(f)| (dB) Phase (°)

Formulas used:
f_c = 1 / (2πRC)
|H(f)| = 1 / √(1 + (f/f_c)²)
φ(f) = −tan⁻¹(f/f_c)
At f = f_c, |H| = −3 dB and φ = −45°.

Resistor Colour Code to Value

Band count

Result

Pick digits and multiplier.

Significant digits

Multiplier / Tolerance / Tempco

PPM/DegC

Formula: ΔV = V_nom × (PPM × ΔT) / 10⁶

This calculates the change in value of any nominal quantity (voltage, frequency, resistance, etc.) for a temperature coefficient specified in ppm/°C.
Note: % = ppm / 10000

Voltage Regulator Capacitor Designer/Helper

Topology:
Vin / Vout:	V / V
I_load (A):
Switching f_sw / L:	/
Transient step ΔI / window Δt:	/
Allowed ΔV_out (Vpp):
ESR estimate (Ω):	per capacitor
Cap type & derating:	Effective factor: (e.g. 0.5–0.7 MLCC at bias)
E-series & units:
Ratings (min):	Vrating headroom: Max parts in parallel to try:

#	Role	N × Cap (nom)	C_eff total	ESR total	Est. ripple / note
Fill the inputs and click Calculate…

Instructions & field help

Topology – Choose LDO for linear regulators (no inductor), or Buck/Boost for switchers.
Vin / Vout – Input/output voltages in volts (V).
I_load – Maximum DC load current in amps (A).
Switching f_sw / L – Converter switching frequency (Hz) and inductor value (H). Used to estimate inductor ripple current.
ΔI / Δt – For LDO transient sizing only: expected load step (A) and the time window the output cap must hold the rail (s).
Allowed ΔV_out – Peak-to-peak ripple or droop you can tolerate at Vout (V_pp). If unsure, 1–2% of Vout is a common starting point.
ESR estimate (Ω) – ESR of a single chosen capacitor at the relevant frequency. Parallel parts reduce ESR: ESR_total ≈ ESR_each/N.
Cap type & derating – Picks technology and the effective factor applied to nominal capacitance:
• MLCC: capacitance falls with DC bias & temp; use 0.5–0.7 as a realistic effective factor at working voltage.
• Electrolytic: value is close to nominal; use 0.8–1.0. Check ripple current rating.
• Tantalum: use 0.8–1.0; ensure surge/derating per datasheet.
E-series & units – Rounds suggestions to E6/E12/E24 preferred values in the unit you like (nF/µF/mF).
Voltage rating headroom – Minimum ratio of part rating to the highest DC across it. Example 1.25× on a 12 V rail ⇒ ≥ 15 V rated parts.
Max parts – Upper bound on how many caps in parallel to consider.

What the results mean

N × Cap (nom) – Number of parallel parts and their nominal value (before derating).
C_eff total – Effective capacitance available after derating and paralleling:
C_eff,total = N × C_nom × effective_factor.
ESR total – Parallel ESR estimate:
ESR_total ≈ ESR_each / N.
Est. ripple / note – First-order ripple (or hold-up) estimate and any rating reminders.

How ripple is estimated

Switching (Buck/Boost) – Output ripple is the sum of a capacitive term and an ESR term:

• Inductor ripple current, rough:

Buck: ΔI_L ≈ (V_in − V_out) · D / (L · f_sw)
Boost: ΔI_L ≈ V_in · D / (L · f_sw), where D = 1 − V_in/V_out

• Ripple from capacitance: ΔV_C ≈ ΔI_L / (8 · C · f_sw)
• Ripple from ESR: ΔV_ESR ≈ ΔI_L · ESR_total
• The tool sizes Cout so ΔV_ESR + ΔV_C ≤ ΔV_{out, allowed}.

Choosing Cin vs Cout

Cout – Controls output ripple and load-step droop. Favor low ESR near the regulator. MLCCs excel for high-frequency ripple; add an electrolytic for bulk if needed.
Cin – Decouples the switch/input pin. For bucks, input RMS current can be significant (worst near D≈0.5). Place low-ESR MLCC(s) close to the switch, and ensure the voltage rating headroom.

Practical tips

Bias derating (MLCC): 10–22 µF parts can lose 30–60% at working voltage; the effective factor accounts for this.
ESR vs stability: Many LDOs require a minimum ESR; some switching controllers specify Cout ESR ranges—always check the datasheet.
Ripple current rating: For electrolytics/tantalum, ensure the capacitor ripple current rating exceeds the expected ripple current.
Thermal & layout: Keep high-di/dt loops tight. Put Cin right at the switch pins; pour ground and use short, wide traces.
Validation: Measure with a short ground spring on the scope probe to avoid ground-lead artifacts.

These are first-order estimates. Final values must satisfy your regulator datasheet (minimum Cout, ESR windows, stability, and ratings).

Non-Inverting Op-Amp Amplifier

Ground Resistor

Rin:

Feedback Resistor

Rf:

Input Voltage

V

Vout: — | Gain: —

Vout vs Vin

Ideal Op-Amp Model:
Gain = 1 + Rf / Rin
Vout = Gain ⋅ Vin
Note: Real op-amps have bandwidth limits, offsets, and saturation; this shows ideal linear amplification.

PPM Deviation

Formula: PPM = (ΔV / V_nom) × 10⁶

This calculator converts between nominal voltage, ppm, and voltage deviation in volts, microvolts, and nanovolts.
Enter any valid pair of values and the related fields will be calculated.

Temperature Coefficient of Resistance (TCR)

Formula: R_T = R₀[1 + α(T − T₀)]

Calculates the resistance of a component at a different temperature using the linear temperature coefficient model.
R₀ is the resistance at reference temperature T₀.

Op-Amp Gain (Inverting)

Formula: A_v = –R_f / R_in

Calculates the voltage gain of an inverting operational amplifier.

The gain is negative because the output is inverted relative to the input.
Typical resistor values range from 1 kΩ to 100 kΩ depending on noise and bandwidth requirements.

Op-Amp Gain (Non-Inverting)

Formula: A_v = 1 + (R_f / R_in)

Calculates the voltage gain of a non-inverting operational amplifier.

The non-inverting amplifier produces an output that is **in phase with the input**.
Gain is always ≥ 1 because of the feedback topology.

Time / Hz

Formula: f = 1 / T and T = 1 / f

Converts between frequency and period.

This calculator converts between frequency in Hz and period in milliseconds.
Frequency and period are reciprocals of each other.

Impedance of R, L, C at frequency f (series)

Formula: Z = √[ R² + (ωL – 1/ωC)² ]

Phase: θ = tan⁻¹((ωL – 1/ωC) / R)

Calculates total impedance of series R, L, C.

Input / Output Values

R (Ω):

L (H):

X_L (Ω):

|Z| (Ω):

f (Hz):

C (F):

X_C (Ω):

∠ (deg):

Calculate

Notes:
This calculator finds the impedance magnitude and phase angle of a series RLC circuit at a chosen frequency.
Inductive reactance is X_L = 2πfL and capacitive reactance is X_C = 1 / (2πfC).
The net reactance is X = X_L − X_C.
A positive phase indicates inductive behaviour, while a negative phase indicates capacitive behaviour.

Energy in a Capacitor

Formula: E = ½·C·V²

Calculates stored energy from capacitance and voltage.

Energy stored in a capacitor depends on capacitance and the square of the applied voltage.
Capacitance is entered in µF and internally converted to Farads.

Energy in an Inductor

Formula: E = ½·L·I²

Calculates stored energy from inductance and current.

Energy stored in an inductor depends on inductance and the square of the current.
Inductance is entered in µH and internally converted to Henries.

SNR (Signal-to-Noise Ratio)

Formula: SNR_dB = 20·log₁₀(V_s/V_n)

Calculates signal-to-noise ratio from signal and noise voltages.

Enter signal voltage and noise voltage to calculate SNR in decibels.

LC Resonant Frequency

Formula: f₀ = 1 / (2π√(LC))

Finds the resonant frequency of an LC circuit.

RC Filter 1st Order

Formula: f_c = 1 / (2πRC)

This calculator solves the 1st-order RC cutoff relationship using any two of resistance, capacitance, and frequency.
Capacitance is entered in uF and frequency is returned in Hz.

Power Supply Ripple (with DC voltage)

Formulae: V_r(pp) ≈ I / (f_ripple · C), f_ripple = f_line (half-wave) or 2·f_line (full-wave)

Enter load current (or V_DC + R), line frequency, capacitance (µF), and rectifier type. Optionally enter V_DC to see ripple % and estimated V_min/V_max.

Input Values

V_DC (V):

R (Ω):

C (µF):

I (A):

f_line (Hz):

Rectifier:

Results

f_ripple (Hz):

Ripple (% of V_DC):

V_min (V):

V_r(pp) (V):

V_max (V):

Calculate

This calculator estimates ripple frequency, peak-to-peak ripple, ripple percentage, and approximate V_min/V_max for a capacitor-input power supply.
If current is left blank, it can be derived from V_DC and load resistance. Full-wave rectifiers ripple at twice the line frequency.

Rectifier Capacitor Ripple

Formula: V_ripple ≈ I / (f·C)

Estimates ripple voltage from load current and smoothing capacitance.

This calculator estimates the peak-to-peak ripple voltage for a rectifier with a smoothing capacitor.
Capacitance is entered in µF and internally converted to Farads.

Wavelength ↔ Frequency ↔ Signal Speed

Formula: λ = v/f f = v/λ v = fλ

Relates signal speed, wavelength, and frequency.

Enter any two values and the third will be calculated.
For electromagnetic waves in free space, signal speed is approximately 299,792,458 m/s.

LED Series Resistor

Input / Output Values

Vs (V):

Vf (V):

If (mA):

LEDs in series (N):

Resistor R (Ω):

Resistor power (W):

Calculate

Notes:
This calculator assumes a simple series resistor feeding one or more LEDs in series.
The resistor value is found from the supply voltage minus the total LED forward voltage, divided by the LED current.
Resistor power is calculated from I²R.
If Vs is less than or equal to N × Vf, there is not enough voltage to drive the LED string correctly.

Capacitor Code ↔ Value

Formula: 3-digit EIA capacitor code → pF / µF, and reverse. Example 104 = 100,000 pF = 0.1 µF

This calculator converts a standard 3-digit capacitor code into capacitance, or estimates the approximate EIA code from a value entered in µF.
Example: 104 means 10 × 10⁴ pF = 100,000 pF = 0.1 µF.

Resistor Colour Code ↔ Value

Formula: Resistor colour code (4 / 5 / 6-band). Works in both directions — enter resistance or colour bands.

Input Values

Resistance (Ω):

Bands:

Tolerance (%):

Temp Coeff (ppm/°C):

Convert

Colour Bands

Colours:

Notes:
For 4-band resistors, the first 2 bands are digits, the 3rd is the multiplier, and the 4th is tolerance.
For 5-band resistors, the first 3 bands are digits, then multiplier and tolerance.
For 6-band resistors, the 6th band gives the temperature coefficient in ppm/°C.
Enter colour names separated by spaces, commas, or hyphens.

Quarter-Wave Resonator

Formula: l = v / (4·f)

Calculates resonant length of a λ/4 resonator.

A quarter-wave resonator has a physical length equal to one quarter of the wavelength of the signal.
For RF in free space, signal speed ≈ 299,792,458 m/s. Transmission lines may use a lower velocity factor.

Transmission Line Impedance

Formula: Z₀ = √(L/C) (L, C per unit length)

Finds characteristic impedance from inductance and capacitance per unit length.

Characteristic impedance depends only on the distributed inductance and capacitance of the transmission line.
Typical values are about 50 Ω for RF coaxial cables and 75 Ω for video and antenna feed lines.

Skin Depth

Formula: δ = √(2ρ / (ωμ)), μ = μ₀μ_r

Computes AC current penetration depth in conductors.

Skin depth is the depth at which AC current density falls to about 37% (1/e) of its value at the conductor surface.

Current Density

Formula: J = I / A

Calculates current per unit area.

Current density describes how much electric current flows through a unit cross-sectional area of a conductor.

Wire Resistance

Formula: R = ρ·l / A

Finds resistance of a wire from length, area, and resistivity.

Calculates the electrical resistance of a conductor using resistivity, length, and cross-sectional area.

Q Factor

Formula: Q = f₀/Δf or Q = X_L/R at f₀

Calculates quality factor of a resonant circuit.

This calculator finds Q either from resonant frequency and bandwidth, or from inductive reactance divided by resistance at the resonant frequency.
Enter either f₀ and Δf, or f₀, R, and L.

Reactance

Formula: X_C = 1/(2πfC), X_L = 2πfL

Computes capacitive and inductive reactance at frequency (Xc, Xl).

This calculator finds capacitive and inductive reactance at a chosen frequency.
Capacitor input is in µF and inductor input is in µH.
Leave either L or C blank if you only want one reactance value.

Reactance

Quick Overview

Reactance is the AC “resistance” of reactive parts: Capacitive X_C = 1/(2πfC) (decreases with f) | Inductive X_L = 2πfL (increases with f). Enter frequency plus C and/or L; if both are given, series resonance f₀ is shown.

Units supported: Hz/kHz/MHz, pF…F, µH…H. Scientific notation like 2.2e-6 works.
Outputs shown in Ω/kΩ/MΩ. Plot is log–log across ±2 decades around the entered frequency.

Frequency (f):		Capacitance (C):
Inductance (L):		DPs & Units:
X_C:		X_L:

dBm ↔ mW / W Conversions

Formula: P(dBm) = 10·log₁₀(P_mW / 1mW)

Formula: P(mW) = 10^(P(dBm)/10)

Formula: P(W) = P(mW) / 1000

Converts between dBm, milliwatts, and watts.

Enter any one value (dBm, mW, or W) and click Solve.
0 dBm = 1 mW.

Battery Life Estimator

Formula: t = (Capacity / Load) × (Efficiency / 100)

Estimates operating time from battery capacity and load current.

Battery life is estimated from battery capacity divided by load current.
Efficiency can be used to account for regulator losses or battery discharge inefficiency.

Power Dissipation

Formula: P = VI or P = I²R or P = V²/R

Computes electrical power from V, I, or R.

Enter any two values (V, I, or R) and the calculator will compute the power.
Uses the three equivalent power formulas: P = VI, P = I²R, and P = V²/R.

dB Conversions (Power & Voltage Ratios)

Formula: dB (power) = 10·log₁₀(P₂/P₁)

Formula: dB (voltage) = 20·log₁₀(V₂/V₁)

Converts power or voltage ratios to and from decibels.

Enter either a ratio or a decibel value and the corresponding value will be calculated.
Use the power formulas for power ratios and the voltage formulas when impedance is constant.

Duty Cycle ↔ On/Off Time

Formula: D = (t_on/T) × 100%

Formula: t_on = D·T, t_off = T – t_on

Converts between duty %, on-time, and off-time. Enter f or T plus duty.

Enter either frequency or period, together with duty cycle, and the calculator will find the corresponding on-time and off-time.
Duty cycle must be between 0% and 100%.

mm ↔ mils

Formula: mils = mm / 0.0254 or mm = mils × 0.0254

Converts metric to imperial PCB dimensions.

1 mil = 0.001 inch = 0.0254 mm.

Digital Multimeter — Uncertainty Specifications

Quick Overview

This tool estimates the measurement uncertainty of a DMM for a given range and reading, using datasheet-style specifications of the form ±(ppm of Reading + ppm of Full-scale), plus optional calibration and temperature terms. It works for voltage, current and resistance ranges, and supports a 3458A-style temperature coefficient of (ppm of reading + ppm of range) per °C.

Range full-scale (FS): Enter the range value (e.g. 10) and choose the unit (V, mA, kΩ, etc.).
Reading (R): Enter the reading in the same unit as FS (the unit label updates automatically).
Applied / Ambient Temp: The temperature at which the measurement is made.
Reference Temp (Tref): The reference temperature of the spec (usually 23 °C or 25 °C).
Spec set: Which datasheet column you are using: 24 Hour, 1 Year, or Custom.
24h / 1y / Custom ppmR & ppmFS: Copy the accuracy line from the datasheet, interpreted as ±(ppmR·R + ppmFS·FS).
Calibration uncertainty: Extra ppm of reading from the Cal. lab (often the “Typical Calibration Uncertainty” column).
Temp coefficient (per °C): Enter ppm of reading and ppm of range per °C (e.g. 3458A style: “(ppm of reading + ppm of range)/°C”).

Error model & results

|ΔT|: |Ambient − Tref| (shown in °C).
E_R (reading term): ppmR · R / 10⁶.
E_FS (full-scale term): ppmFS · FS / 10⁶.
E_cal (calibration): ppmCal · R / 10⁶.
E_T (temperature): (ppmTC_R·R + ppmTC_FS·FS) · |ΔT| / 10⁶.
Worst-case |E|: |E_R| + |E_FS| + |E_cal| + |E_T| (same units as FS / R).
RSS “typical” (root-sum-square) |E|: √(E_R² + E_FS² + E_cal² + E_T²).
Displayed (WC): R ± |E|, i.e. the reading range that covers the worst-case error.
Total spec (ppm): The total worst-case error expressed in ppm of the reading: |E| / R × 10⁶. This normalizes the uncertainty so different readings, ranges, and functions can be compared directly.

Note: Leave unused entries blank or set to zero.

Inputs

Range full-scale (FS):

Reading (R):

V

Applied / Ambient Temp:

°C

Reference Temp (Tref):

°C

Spec set:

24h: ±(ppmR + ppmFS)

ppmR ppmFS

1y: ±(ppmR + ppmFS)

ppmR ppmFS

Custom:

ppmR ppmFS

Calibration uncertainty:

ppm of reading

Temp coefficient (per °C):

ppmR/°C ppmFS/°C

Results

|ΔT| = |Ambient − Tref|:

-

E_R (reading term):

-

E_FS (full-scale):

-

E_cal:

-

E_T (temp):

-

Worst-case |E|:

-

RSS “typical” |E|:

-

Displayed (WC):

-

Total spec (ppm):

-

Error term formulas:
• E_R = (ppmR × R) / 10⁶ Reading-dependent uncertainty
• E_FS = (ppmFS × FS) / 10⁶ Full-scale (range) uncertainty
• E_cal = (ppmCal × R) / 10⁶ Calibration reference contribution
• E_T = [(ppmTC_R × R) + (ppmTC_FS × FS)] × |ΔT| / 10⁶ Temperature coefficient applied to the reading and the range

Combination rules:
• Worst-case: |E_R| + |E_FS| + |E_cal| + |E_T| All error sources assumed to add in the same direction
• RSS (typical): √(E_R² + E_FS² + E_cal² + E_T²) Statistical combination; typical real-world performance

SMPS — Duty, Inductor Ripple & Output Ripple

Quick Overview

A buck SMPS reduces a higher input voltage V_in to a lower V_out using a switch, diode/MOSFET, inductor, and output capacitor. This tool assumes ideal parts and CCM (the inductor current never reaches zero). Results update automatically as you type.

f_s: Switching frequency.
Duty D: On-time fraction (ideal buck: D ≈ V_out/V_in).
ΔI_L (pp): Inductor current ripple, peak-to-peak.
I_pk / I_valley: Max/min inductor current each cycle (average equals load current).
L (~30% ripple): Inductance that gives ~30% ripple at the entered load and f_s.
ΔV_ESR: Ripple from the capacitor ESR (ΔV = ΔI_L · ESR).
ΔV_C: Capacitive ripple from charge/discharge (ΔV = ΔI_L / (8 · f_s · C)).
ΔV_total (pp): Simulated time-domain ripple (ESR + capacitive).
CCM check: CCM holds if I_out > ΔI_L/2.

Inputs

V_IN:

V

V_OUT:

V

I_OUT:

A

f_s:

L:

C (output):

ESR (cap):

V_ripple target:

mVpp

Results (ideal)

f_s:

-

Duty D:

-

ΔI_L (pp):

-

I_pk:

-

I_valley:

-

L (~30% ripple):

-

ΔV_ESR:

-

ΔV_C:

-

ΔV_total (pp):

-

C needed @ target:

-

Inductor Current (IL) Scale: pp: -

Output Voltage Ripple Scale: pp: -

SW Node Voltage (Vsw)

555 Timer (Astable) - Mark/Space & Duty

Timing Components

R_A:

R_B:

C:

Show capacitor ramp (pin 2/6)

Results

f:

—

Duty:

—

Mark:Space:

—

t_H:

—

t_L:

—

T:

—

f = 1.44 / ((R_A + 2R_B)·C), t_H = 0.693(R_A + R_B)·C, t_L = 0.693 R_B·C, D = (R_A + R_B)/(R_A + 2R_B)

Schematic — 555 Astable

555 Timer (Astable) Frequency & Duty

Formula: f = 1.44 / ((R_A + 2R_B)C)

Duty: D = (R_A + R_B) / (R_A + 2R_B) × 100%

t_H: 0.693(R_A + R_B)C, t_L: 0.693R_BC

Calculates timing values for a 555 astable.

This calculator gives the oscillation frequency, duty cycle, high time, low time, and period for a 555 timer in astable mode.
Capacitance is entered in uF and internally converted to Farads.

Joule ↔ Watt-hour

Formula: 1 Wh = 3600 J

Converts between Joules and Watt-hours.

This calculator converts energy between Joules and Watt-hours.
1 Watt-hour equals 3600 Joules.

Voltage Divider

Formula: Vout = Vin × (R2 / (R1 + R2))

Schematic

Joule’s Law — P = I²R

Quick Overview

Joule’s Law defines the electrical power dissipated as heat in a conductor when current flows through it. The law states that the power (P) developed in a resistor is proportional to the square of the current (I) and the resistance (R): P = I²R. This principle forms the basis for calculating energy losses in resistors, heating elements, and conductors.

Formula: P = I² × R
P = Power (Watts)
I = Current (Amperes)
R = Resistance (Ohms)

Example: If a current of 2.5 A flows through a 4 Ω resistor, then P = (2.5)² × 4 = 25.0 W.

Lenz’s Law

Quick Overview

Lenz’s Law describes the direction of an induced electromotive force (EMF) caused by a changing magnetic field. It states that the induced EMF will always act to oppose the change in magnetic flux that produced it. The negative sign in the equation reflects this opposition — ensuring energy conservation and preventing self-reinforcement of the magnetic field.

Formula: E = −N × (dΦ/dt)
E = Induced EMF (Volts)
N = Number of turns in the coil
dΦ/dt = Rate of change of magnetic flux (Webers per second)

Example: If a 200-turn coil experiences a flux change rate of 0.015 Wb/s, then E = −200 × 0.015 = −3.0 V (the negative sign shows the opposing direction).

Kirchhoff’s Laws

KCL: ΣI_in − ΣI_out = 0 | KVL: ΣV(loop) = 0

Quick Overview

Kirchhoff’s Laws are two fundamental principles of electrical circuit analysis. They describe how current and voltage distribute within any network. Kirchhoff’s Current Law (KCL) states that the total current entering a junction equals the total current leaving it, ensuring charge conservation. Kirchhoff’s Voltage Law (KVL) states that the sum of all voltage rises and drops around a closed loop is zero, conserving energy. Together, these laws provide the foundation for solving even the most complex DC and AC circuits.

Kirchhoff’s Current Law (KCL): At any node, total current entering = total current leaving.
Kirchhoff’s Voltage Law (KVL): Around any closed loop, total voltage drops = total rises.

KCL — Node Current Balance

Use sign convention: + = current into node, − = out of node. Leave one field blank to solve the unknown, or fill all to check ΣI = 0.

Example: +2.5 A, −1.2 A, ? → Unknown = −(2.5 − 1.2) = −1.3 A (i.e. 1.3 A out).

KVL — Loop Voltage Sum

Use sign convention: + = drop, − = source/rise. Leave one field blank to solve the missing voltage or fill all to verify ΣV = 0.

Example: −12 V (source), +7.2 V (drop), ? → Unknown = −(−12 + 7.2) = +4.8 V (drop).

Tips & FAQ

Use scientific notation (e.g. 2.5e-3 for 2.5 mA).
KCL satisfied → currents balance to 0 A.
KVL satisfied → voltage drops and rises sum to 0 V.
Check units: mA vs A, mV vs V, etc.

Parallel Resistors

Formula: 1/R_eq = 1/R₁ + 1/R₂ + … + 1/R_n

R1:		R2:
R3:		R4:
R5:		R6:
R7:		R8:
Total Resistance:
DPs: Output units:

Reverse (desired total): E-series: Maximum no. resistors to combine: Show best for each resistor count

LM317 Regulator

Formula (LM317): V_out = V_ref(1 + R₂/R₁) + I_adj·R₂

Calculates output voltage of LM317 regulator.

Enter any two of R1, R2, and V_out, and the third value will be calculated.
Default values are the usual LM317 reference voltage of 1.25 V and a typical adjust pin current of 50 µA.

LM337 Regulator

Formula (LM337): V_out = V_ref(1 + R₂/R₁) + I_adj·R₂ (typ. V_ref ≈ –1.25 V)

Calculates output voltage of LM337 regulator.

Enter any two of R1, R2, and V_out, and the third value will be calculated.
This follows the same equation style as LM317, but with the LM337’s negative reference value.

RC Charge/Discharge

Quick Overview

In a simple RC circuit, the capacitor voltage follows an exponential curve with time constant τ = R × C. A general form that covers both charging and discharging is: V_C(t) = V_f + (V₀ − V_f) · e^−t/(RC), where V₀ is the initial capacitor voltage at t=0, and V_f is the final voltage the capacitor is heading toward (for charging, V_f=V_S; for discharging to ground, V_f=0).

Charging: V_C(t) = V_S − (V_S − V₀) e^−t/RC
Discharging: V_C(t) = V₀ e^−t/RC (toward 0 V)
At t = τ, charging reaches ≈63.2% of the final step; discharging falls to ≈36.8% of the initial value.
Enter values using handy units (kΩ, µF, ms, etc.). Use scientific notation like 2.2e-6 if you prefer.

Mode:
Supply (V_S):	(ignored in Discharge)	Initial (V₀):
Resistance (R):		Capacitance (C):
Time (t):		Target V_C (optional):
DPs:

Faraday’s Law of Electromagnetic Induction

Quick Overview

Faraday’s Law describes how a changing magnetic field induces an electromotive force (EMF) in a coil or conductor. The magnitude of the induced EMF is proportional to the rate of change of magnetic flux and the number of turns in the coil: E = −N × (ΔΦ / Δt). The negative sign represents Lenz’s Law — the induced EMF opposes the change that produced it.

E = Induced EMF (Volts)
N = Number of turns in the coil
ΔΦ = Change in magnetic flux (Webers)
Δt = Time interval (seconds)
Enter any three values to solve for the fourth.

Example: N = 200 turns, ΔΦ = 0.015 Wb, Δt = 0.05 s → E = N × (ΔΦ / Δt) = 200 × (0.015 / 0.05) = 60 V.

Ohm’s Law

Quick Overview

Ohm’s Law relates voltage (V), current (I), and resistance (R) in any electrical circuit: V = I × R, I = V / R, R = V / I. Power ties in via P = V × I = I²R = V²/R. Enter any two values to compute the other two.

Use scientific notation (e.g. 2.5e-3 for 2.5 mA).
Pick convenient units from the dropdowns; results are written using the selected units.
If you provide more than two inputs, the first valid pair in priority (V&I → V&R → I&R → P&V → P&I → P&R) is used.

Example: V = 12 V, R = 4.7 kΩ → I = 12 / 4700 = 2.553 mA, P = 12 × 2.553 mA ≈ 30.6 mW.

Biot–Savart Law

Quick Overview

The Biot–Savart Law gives the magnetic field contribution from current elements: dB = (μ₀ μ_r / 4π) · (I dℓ × r̂) / r².
Biot-Savart Law is one of the big four Maxwell's equations.
For common symmetric shapes this integrates to compact formulas:

Loop (center): B = μ₀ μ_r N I / (2R)
Loop on-axis (distance x): B = μ₀ μ_r N I R² / [2(R² + x²)^{3/2}]
Finite straight wire (length L, point at r from midpoint): B = (μ₀ μ_r I / 4πr) · (L / √(r² + (L/2)²))
Circular arc (angle φ): B = μ₀ μ_r N I φ / (4πR) (φ in radians)

Constants: μ₀ = 4π×10⁻⁷ H/m. Use μ_r=1 for air/vacuum. Outputs show both B (tesla) and H (A/m), with B = μ·H.

Geometry:
μ_r (relative):		(dimensionless)
Turns N:		Current I:
Radius R:		Field at loop center
Turns N:		Current I:
Radius R:		Axial x:
Current I:		Length L:
Perp. distance r:		(Point lies on line normal through wire midpoint)
Turns N:		Current I:
Radius R:		Angle φ (deg):
DPs:
B-field:		H-field:

Ampère’s Law

Quick Overview

Ampère’s Law (magnetostatics) relates the circulation of the magnetic field around a closed loop to the total current enclosed: ∮ B·dℓ = μ₀ μ_r I_enc.
Ampère's Law is one of the big four Maxwell's equations.
With symmetry, this gives handy field formulas:

Long straight wire: B = μ₀ μ_r I / (2π r)
Long solenoid (inside): B = μ₀ μ_r n I, where n = N/L
Toroid (mean radius r): B(r) = μ₀ μ_r N I / (2π r)

Constants: μ₀ = 4π×10⁻⁷ H/m. Use μ_r=1 for air/vacuum. Outputs show both B (tesla) and H (A/m), with B = μ·H.

Geometry:
μ_r (relative):		(dimensionless, e.g. air=1, ferrite ~ 100–2000)
Current I:		Radius r:
Turns N:		Length L:
Current I:		(Assumes long solenoid, field near center)
Turns N:		Current I:
Radius r (point):		(Field valid for r between inner & outer radii)
DPs:
B-field:		H-field:

Gauss’s Law

Quick Overview

Gauss’s Law relates total electric flux through a closed surface to the enclosed charge: ∮ E·dA = Q_enclosed/ε₀. It’s most useful for highly symmetric fields.
Gauss's Law is one of the big four Maxwell's equations.

Flux–Charge: Φ = Q/ε₀, Q = ε₀Φ
Symmetric fields: Sphere: E = Q/(4π ε₀ r²) · r̂ | Line: E = λ/(2π ε₀ r) · r̂ | Plane: E = σ/(2ε₀) n̂
ε₀ = 8.854 187 812 8 × 10⁻¹² F·m⁻¹

Mode:
Geometry:
Charge Q:	Flux Φ:	(N·m²/C)
Charge Q (sphere):	Radius r (sphere):
Line charge λ:	Radius r (line):
Cylinder length L:	(Affects flux via Q_enc=λ·L; E depends only on r)
Surface charge σ:	Area A (optional):
DPs:
Electric field E:	Flux Φ:

Coulomb’s Law

Quick Overview

Coulomb’s Law describes the electric force between two point charges. The magnitude of the electrostatic force is proportional to the product of the charges and inversely proportional to the square of their separation distance.
Coulomb's Law is one of the big four Maxwell's equations.

Formula: F = k · |q₁ · q₂| / r²
where k = 8.9875×10⁹ N·m²/C², q₁ and q₂ are charges in coulombs, and r is distance in meters.

Positive force ⇒ repulsion (like charges)
Negative force ⇒ attraction (opposite charges)

Zener Diode

Formula: V_out ≈ V_Z, R_s = (V_in – V_Z) / (I_Z + I_L)

Calculates series resistor and power dissipation.

Input Values

Max Input:

Volts

Min Input:

Volts

Output:

Volts

Load:

mA

Calculate

Results

Resistor:

Ohms

Resistor:

Watts

Zener:

Volts

Zener:

Watts

This calculator estimates the required series resistor and the approximate power dissipated in both the resistor and zener diode.
It assumes a simple zener regulator with about 10 mA additional zener current margin.

Decimal ↔ Scientific Converter

Converter: Decimal ↔ Scientific (a × 10^b)

Converts between decimal and scientific notation.

Enter either a decimal value, or a mantissa and exponent, and the converter will calculate the other form.
Significant digits control the rounding of the scientific notation result.

DC Power Supply Efficiency

Formula: η (%) = 100 · (V_outI_out) / (V_inI_in)

Enter three or four values and the calculator will work out the missing electrical quantity, input power, output power, efficiency, and power loss.
Efficiency is calculated from output power divided by input power.

Voltage Drop (wire/cable), % drop & loss

Formula: R = ρ·L/A, V_drop = I·R, P_loss = I²R

Input Values

Current (A):

Area (mm²):

System V (optional):

Length one-way (m):

Material:

include return (2×L)

Results

Resistance (Ω):

P_loss (W):

V_drop (V):

% of System V:

Calculate

This calculator estimates cable resistance, voltage drop, power loss, and percentage voltage drop.
Length is entered as one-way distance. Tick the return option for the full loop length. Copper and aluminium resistivity values are assumed at about 20°C.

Decimal ↔ mA, µA/uA, nA, pA and mV, µV/uV, nV, pV ↔ Scientific

Converter: mA / µA / nA / pA and mV / µV / nV / pV ↔ Scientific (a×10^b)

Converts SI-prefixed values to and from scientific notation.

Prefixed Value Input

Value with unit:

Scientific Form

Scientific:

× 10^

Unit:

Results

SI (base):

Best prefix:

Calculate

Enter a prefixed value such as 100mA, 2.5uA, or 350nV, or enter mantissa and exponent to convert the other way.
Supported prefixes are m, µ/u, n, and p. Outputs are shown in base SI units and in a best-fit prefixed form.

RLC Impedance (series/parallel) → |Z| and phase

Input / Output Values

Mode:

R (Ω):

C (F):

Phase (°):

f (Hz):

L (H):

|Z| (Ω):

Calculate

Notes:
In series mode, the impedance is found from resistance and net reactance: X = ωL − 1/(ωC).
In parallel mode, the calculation is done from the total admittance and then converted back to impedance magnitude.
The phase angle is shown in degrees.
A positive phase means inductive behaviour; a negative phase means capacitive behaviour.

RC Charging/Discharging (time ↔ % of Vin)

Induced EMF (E):	V
Coil Turns (N):
Rate of Flux Change (dΦ/dt):	Wb/s

EMF (E):	V	Turns (N):
Flux Change (ΔΦ):	Wb	Time Interval (Δt):	s
DPs:

Voltage (V):		Current (I):
Resistance (R):		Power (P):
DPs:

Charge q₁ (C):
Charge q₂ (C):
Distance r (m):

Force (N):