Basic calculations

Alternating current, impedance, reactance calculations

Signals, systems
Decibel, power ratio calculations

Inductors

Capacitors

Integrated circuits, oscillators, timers

Thermals

This tool is provided without any warranty.
Supported unit prefixes:
Add unit prefix as a suffix to the number, for example: 1M.
 f p n u m c k M G T P femto pico nano micro milli centi (none) kilo mega giga tera peta 10-15 10-12 10-9 10-6 10-3 10-2 100 103 106 109 1012 1015

For squared quantities (for example areas), only the following suffixes are supported: u, m, c, k, M

## Ohm's law

Enter two quantities, the third one will be calculated
$R = \dfrac{V}{I}$
 Voltage V Resistance Ω Current A

## Power (for DC circuits)

Enter two quantities, the third one will be calculated
$P = V \cdot I$
 Voltage V Current A Power W

## Power (for DC circuits)

Enter two quantities, the third one will be calculated
$P = V \cdot I \cdot \mathrm{cos}(\phi)$
$Q = V \cdot I \cdot \mathrm{cos}(\phi)$
$|S| = V_{rms} \cdot I_{rms}$
 Input quantities: Voltage V Current A Phase angle degrees radians Output quantities: Real (active) power W Reactive power var Apparent power VA

## E6/E12/E24 series (IEC 60063 standard)

 Input quantities: Value Series: E6 E12 E24 Output quantities: Closest lower or equal match Closest higher or equal match Closest match

## LED resistor calculator

$R = \dfrac{V_{in}-V_{LED}}{I_{LED}}$
 Input quantities: Desired current A Input voltage V LED voltage V Resistor series: Don't care E6 E12 E24 Output quantities: Calculated resistance Ω Calculated dissipation W Nearest bigger resistor: Ω New LED current*: A * with nearest bigger resistor

## Capacitance / 3 digit code conversion

Enter either capacitance or code, the other value will be auto-calculated
Allowable range: 10pF to 99mF (although capacitors bigger than 10uF usually aren't marked this way)
 Code Capacitance F
 Letter B C D F G J K M Z Tolerance ±0.1pF ±0.25pF ±0.5pF ±1% ±2% ±5% ±10% ±20% +80, -20%

## Capacitor reactance

Enter two quantities, the third one will be calculated
$X_C = \dfrac{1}{2 \cdot \mathrm{\pi} \cdot f \cdot C}$
 Capacitance F Frequency Hz Reactance Ω

## Inductor reactance

Enter two quantities, the third one will be calculated
$X_L = 2 \cdot \mathrm{\pi} \cdot f \cdot L$
 Inductance H Frequency Hz Reactance Ω

## RLC circuit impedance

$X_L = 2 \cdot \mathrm{\pi} \cdot f \cdot L$
$X_C = \dfrac{1}{2 \cdot \mathrm{\pi} \cdot f \cdot C}$
Serial:
$Z = R + j \cdot 2 \cdot \mathrm{\pi} \cdot f \cdot L - \dfrac{j}{2 \cdot \mathrm{\pi} \cdot f \cdot C}$
$|Z| = \sqrt{R^2+(X_L-X_C)^2}$
If $X_L > X_C$, then $\phi = \mathrm{arccos} (\dfrac{R}{|Z|})$
If $X_L < X_C$, then $\phi = -\mathrm{arccos} (\dfrac{R}{|Z|})$
Parallel:
$|Z| = \dfrac{1}{\sqrt{\frac{1}{R^2} + (\frac{1}{X_L}-\frac{1}{X_C})^2}}$
$\phi = \mathrm{arctan} (\dfrac{R}{\frac{1}{\frac{1}{X_L} - \frac{1}{X_C}}})$
 Input quantities: Resistance Ω Inductance H Capacitance F Frequency Hz Type: Parallel Serial Output quantities: Capacitor reactance Ω Inductor reactance Ω Impedance Ω Imaginary impedance part Ω Phase shift rad Phase shift °

## Resonant frequency

Enter two quantities, the third one will be calculated.
$f_r = \dfrac{1}{2 \cdot \mathrm{\pi} \cdot \sqrt{ L \cdot C}}$
 Inductance H Capacitance F Frequency Hz

## Critical damping (aperiodic) resistor for RLC circuit

Input quantities:
$Q < 0.5$ ($Q=\dfrac{R}{Z_0}$ for parallel circuit, $Q=\dfrac{Z_0}{R}$ for series circuit, $Z_0 = \sqrt{\dfrac{L}{C}}$)
 Inductance H Capacitance F Type: Parallel Serial Result: Resistance: 0Ω

## Capacitor peak dv/dt, peak current

Enter two quantities, the third one will be calculated.
$I_{max}=C \cdot {\mathrm{max}(\dfrac{\mathrm{d}v(t)}{\mathrm{d}t})}$
 Capacitance F dv/dt V/μs Max. current A

## Sine wave dv/dt (di/dt)

Enter two quantities, the other one will be calculated.
$\mathrm{max} \dfrac{\mathrm{d}v(t)}{\mathrm{d}t} = 2 \cdot \mathrm{\pi} \cdot f \cdot V_m$
 Amplitude V (A) dv/dt or di/dt V/s (A/s) Frequency Hz

## Sine wave amplitude ↔ RMS

Enter one quantity, the other one will be calculated.
$V_{pk} = \sqrt{2} \cdot V_{rms}$
 Amplitude V (A) RMS V (A)

## Rise time, bandwidth

Select encoding/use, enter one quantity, the other one will be calculated.
Assuming first order system, 3 dB permissible attenuation at max. frequency, 10% to 90% rise time, some rounding is done.
NRZ/RZ = (Non) Return-To-Zero
$t_r = \dfrac{0.35}{BW} \mathrm{(RZ)}, t_r = \dfrac{0.7}{BW} \mathrm{(NRZ)}$
 Encoding/use (RZ/NRZ/analog): Analog circuits or RZ encoding NRZ encoding Rise time s Bandwidth/max. freq.: Hz/Baud

## RC low-pass filter

Enter three quantities, the fourth one will be calculated.
 Input/output quantities: Resistance Ω Capacitance F Frequency Hz Attenuation dB Output quantities: Phase angle °

## RC high-pass filter

Enter three quantities, the fourth one will be calculated.
 Input/output quantities: Resistance Ω Capacitance F Frequency Hz Attenuation dB Output quantities: Phase angle °

## Power ratio / decibel conversion

Input one quantity, the other one will be calculated.
$\mathrm{ratio (dB)} = 10 \cdot \mathrm{lg(ratio)}$
 Power ratio dB

## Voltage ratio / decibel conversion

Enter one quantity, the other one will be calculated.
$\mathrm{ratio (dB)} = 20 \cdot \mathrm{lg(ratio)}$
 Voltage ratio dB

## Power / dBm conversion

Enter one quantity, the other one will be calculated.
$P = 10^{(0.1 \cdot ({P_{dBm}-30}))}$
 Power W dBm

## Inductor current rise

$\mathrm{\Delta}I = \dfrac{V \cdot \mathrm{\Delta} T}{L}$
 Input quantities: Inductance H Voltage V Δ time s Output quantities: Δ current A

## Toroid inductance/turns

Enter either inductance or turn count, the other quantity will be automatically calculated.
$L = \dfrac{\mu_r \cdot \mathrm{\mu_0} \cdot N^2 \cdot S}{\mathrm{\pi} \cdot d}$
 Input quantities: Permeability Relative Absolute Permeability Outer diameter m Inner diameter m Height m Cross section Square Circular (circular cross-section is calculated from the diameters) Input/output quantities: Inductance H Turns

## Capacitor voltage rise

$\mathrm{\Delta}V = \dfrac{I \cdot \mathrm{\Delta} T}{C}$
 Input quantities: Capacitance F Current A Δ time s Output quantities: Δ voltage V

## Capacitance

Enter three quantities, the other one will be calculated.
$C = \dfrac{S \cdot \epsilon_r \cdot \mathrm{\epsilon_0} }{l}$
 Permittivity Relative Absolute Permittivity Area m2 Distance m Capacitance F

## Capacitor charge

Enter five quantities, the other one will be automatically calculated
$\tau = R \cdot C$
$t_{total} = \tau \cdot \mathrm{ln} (\dfrac{V_{supply} - V_{initial}}{V_{supply} - V_{final}})$
$V_{final} = V_{initial} + (V_{supply} - V_{initial}) \cdot (1-e^{-t/\tau})$
 Input/output quantities: Capacitance F Resistance Ω Supply voltage V Initial voltage V Final voltage V Time s Output quantities: Tau constant Initial current A Final current A

## Capacitor discharge

Enter four quantities, the other one will be automatically calculated
$\tau = R \cdot C$
$V_{final} = V_{initial} \cdot (1-e^{-t/\tau})$
 Input/output quantities: Capacitance F Resistance Ω Initial voltage V Final voltage V Time s Output quantities: Tau constant Initial current A Final current A

## Capacitor stored energy

Enter two quantities, the third one will be automatically calculated
$E = 0.5 \cdot C \cdot V^2$
 Capacitance F Voltage V Energy J

## ESR ↔ tan δ

Enter the frequency, capacitance and either ESR or tan δ
$ESR = X_C \cdot \mathrm{tan}( \delta)$
 Frequency Hz Capacitance F ESR Ω tan δ [0-1]

## Two transistor astable multivibrator

$\tau_1 = R_2 \cdot C_1$
$\tau_2 = R_3 \cdot C_2$
$t_1 = \tau_1 \cdot \mathrm{ln} (\dfrac{2 V_{CC}}{V_{CC}-V_{BE_{sat}}})$
$t_2 = \tau_1 \cdot \mathrm{ln} (\dfrac{2 V_{CC}}{V_{CC}-V_{BE_{sat}}})$
$f=\dfrac{1}{t_1 + t_2}$
Schematic
 Input quantities: R2 Ω R3 Ω C1 F C2 F Voltages: Ignore Use during calculation VBEsat V VCC V Output quantities: Frequency Hz HIGH time s LOW time s

## Astable 555 frequency/duty cycle

A duty cycle lower than 50% can be achieved by connecting a diode in parallel to R2.
$V_{ctrl}$ $=$ Control voltage $(\dfrac{\% \mathrm{~of~} V_{CC}}{100})$
No diode parallel to R2: $T_{low} = \mathrm{ln}(2) \cdot R_2 \cdot C$
No diode parallel to R2: $T_{high} = (\mathrm{ln}(\dfrac{1-0.5\cdot {V_{ctrl}}}{1-V_{ctrl}}) \cdot (R1+R2) \cdot C$
Diode parallel to R2: $T_{high} = (\mathrm{ln}(\dfrac{1-0.5\cdot {V_{ctrl}}}{1-V_{ctrl}}) \cdot R1 \cdot C$ (diode drop is neglected)
$T = T_{low} + T_{high}$
$f = \dfrac{1}{T}$
$\mathrm{Duty} (\%) = 100\cdot \dfrac{T_{high}}{T}$
 Input quantities: R1 (VCC to DIS) Ω R2 (DIS to THR, TR) Ω C F Diode parallel to R2 no yes Control voltage % of VCC Output quantities: Frequency Hz HIGH time s LOW time s Duty cycle %

## Monostable 555 period

$V_{ctrl}$ $=$ Control voltage $(\dfrac{\% \mathrm{~of~} V_{CC}}{100})$
$T = -\mathrm{ln}(1-V_{ctrl}) \cdot R \cdot C$
 Input quantities: Resistor: Ω Capacitor: F Control voltage % of VCC Output quantities: Period: s

## IR(S)2153(1)(D) frequency

$f \approx \dfrac{1}{1.4 \cdot (R_t+75) \cdot C_t}$
 Input quantities: Timing resistor: Ω Timing capacitor: F Output quantities: Frequency Hz

## UC3842, UC3843, UC3844, UC3845 frequency

The result may not be accurate if the timing resistor is lower than 5kΩ
$f_{osc} \approx \dfrac{1.8}{R_t \cdot C_t}$
 Input quantities: Timing resistor: Ω Timing capacitor: F Chip: UC3842/UC3843 UC3844/UC3845 Output quantities: Oscillator frequency Hz Output frequency Hz

## TL494/KA7500 frequency

$f_{osc} \approx \dfrac{1}{R_t \cdot C_t}$
 Input quantities: Timing resistor: Ω Timing capacitor: F Mode: Single ended Push-pull Output quantities: Oscillator frequency Hz Output frequency Hz

## Voltage regulator feedback

Enter three quantities, the other one will be auto-calculated
$V_{out} = V_{ref} \cdot (\dfrac{R2}{R1}+1)$
 Chip Voltage LM317T 1.25V MC34063 1.25V LM2576-ADJ 1.23V LM2596-ADJ 1.23V UC384x (VFB) 2.5V
 R1: Ω (Reference drop) R2: Ω Reference voltage: V Output voltage: V

## MOSFET, IGBT, diode switching loss calculator, SEMIKRON AN1403 method

Calculate conduction loss separately (approximately IRMS*resistance for FETs, or IAVG for diodes and IGBTs). Gate drive loss is neglected.
The "scaling factor" KS is not included in the Semikron PDF. According to simulations, if a MOSFET has a certain switching loss with certain gate drive resistance (external+internal gate resistance) and it is doubled, the loss will be also roughly doubled (Ks≈2). The MOSFET coefficients also aren't present in the original PDF and were determined empirically through simulations. Switch and diode losses must be calculated separately.
Calculate turn-on and turn-off losses separately and add the results. Diode turn-on losses are usually neglectable compared to conduction and turn-off.

$P_{sw} = f \cdot E_{ref} \cdot (\dfrac{I}{I_{ref}})^{K_I} \cdot (\dfrac{V}{V_{ref}})^{K_V} \cdot (1 + K_T \cdot (T-T_{ref})) \cdot K_S$
 Part type: Typical IGBT (Ki=1, Kv=1.3, Kt=0.003) Typical MOSFET (Ki=1, Kv=1.15, Kt=0.008) Typical diode (Ki=0.5, Kv=0.6, Kt=0.006) Use custom coefficients Select "custom" to adjust Kx Switching loss (energy) at Vref, Iref J Reference current A Reference voltage V Reference temperature: °C Current: A Voltage: V Junction temperature: °C Frequency: Hz Custom Ki: Custom Kv: Custom Kt: Scaling factor: Power dissipation: 0W

## MOSFET switching loss estimation

Calculate conduction loss separately (approximately IRMS*resistance for FETs, or IAVG for diodes and IGBTs).
Switch and diode (internal diode - if it conducts) losses must be also calculated separately.
Don't forget to add prefixes, times are usually in nanoseconds.
The gate resistance effect (tr, tf depend on Rg) calculation is usable only if the gate drive voltage is close to the reference.
If only a light load is switched at a high frequency, it might be a good idea to add the D-S capacitance discharge loss. However, this capacitance might also reduce turn-off loss.
The coefficients were determined theoretically by linearizing the waveform and integrating instantaneous power through the switching times while rising/falling. Select "Custom" in dropdown menus to use custom Kl.

$K_g = \dfrac{R_{g\_{int}}+R_{g\_{ext}}}{R_{g\_{int}}+R_{{g\_{ext}}\_{ref}}}$
$E_{cap} = 0.5 \cdot C_{oss} \cdot {V^2_{ds\_{off}}}$
${E_{sw}}_{on} = K_c \cdot K_g \cdot K_l \cdot t_r \cdot {V_{ds\_on}} \cdot {I_{d\_on}}$
${E_{sw}}_{off} = K_c \cdot K_g \cdot K_l \cdot t_f \cdot {V_{ds\_off}} \cdot {I_{d\_off}}$
$P_{sw} = f*({E_{sw\_on}}+{E_{sw\_off}}+E_{cap})$
 Switching frequency Hz Reference rise time s Reference fall time s Turn-on drain-source voltage V Turn-on drain current A Turn-off drain-source voltage V Turn-off drain current A Consider gate resistor: Consider gate resistance effect on tr, tf Neglect gate resistance effect on tr, tf External gate resistance Ω Reference ext. gate resistance Ω Internal gate resistance Ω Consider Cds: Consider drain-source capacitance Neglect drain-source capacitance Drain-source capacitance F Turn-on load: Resistive (Kl≈0.17) Inductive/Constant current (Kl≈0.5) Custom coefficient Turn-off load: Resistive (Kl≈0.17) Inductive/Constant current (Kl≈0.5) Custom coefficient Custom Kl coefficient, turn-on Custom Kl coefficient, turn-off Custom Esw scaling factor KC: Power dissipation: 0W

## MOSFET/IGBT gate drive loss

$P_{gd} = f \cdot V_{gs\_s} \cdot Q_g$
 Frequency: Hz Gate voltage swing: V Gate charge: C Power dissipation: 0W

## MOSFET, IGBT, diode, resistor conduction loss calculator

Enter only quantities related to the waveform and part type
This function (conduction loss for various waveforms) is still UNDER CONSTRUCTION and might not be accurate.
For simplicity, constant voltage drop is assumed for diodes, constant resistance is assumed for MOSFETs.
${P_{D,IGBT}} \approx V_{drop} \cdot I_{ARV}$
$P_{MOSFET} \approx R \cdot I^2_{RMS}$
Table
* this is only a fairly rough estimation (error ≤6.7%), valid only for Imt<5*Ims
Multiply RMS value of sine/triangle by sqrt(2) to get RMS value of half-rectified sine/triangle
Ims refers to sine amplitude, Imt to triangle amplitude.
 Waveform $I_{RMS}$ $I_{ARV}$ Sine $0.7071 \cdot I_m$ $0.6366 \cdot I_m$ Triangle $0.5774 \cdot I_m$ $0.5 \cdot I_m$ Square, D=0 to 1 $\sqrt{D \cdot I_{high}^2 +(1-D)\cdot I_{low}^2}$ $D \cdot I_{high} \\+ (1-D) \cdot I_{low}$ Superposed triangle and sine, min. at t=0 $\sqrt{I_{rms}^2} \\ I_{rms}^2 = \\ (0.5372 \cdot I_{mt} \\ +0.7071*I_{ms})^2 \\ +(0.0699*I_{mt})^2$ $0.6366 \cdot I_{ms} \\ + 0.5 \cdot I_{mt}$ Superposed triangle and sine, tri. +max. at t=0 $\sqrt{I^2_{rms}} \\ I_{rms}^2 = \\ ((0.5774*I_{mt})^2 \\ +(0.7071*I_{ms})^2)$ $I_{ms} \cdot (0.62+0.2338*(\frac{I_{mt}}{I{ms}}) \\ +0.0403 \cdot (\frac{I_{mt}}{I_{ms}})^2 \\ -0.002\cdot(\frac{I_{mt}}{I{ms}})^3)$  (*)
 Part type: Diode/IGBT (consider constant V) MOSFET (consider constant R) Waveform: Rectangular wave with given duty cycle Sine wave Half rectified sine wave Triangle wave Half rectified triangle wave Superposed sine and triangle, both minimums at t=0 Superposed half-sine and half-triangle, both minimums at t=0 Superposed half-sine and half-triangle, triangle maximum at t=0 Custom average current (for IGBT/D) or RMS current (for MOSFET) Rectangular wave, low current: A Rectangular wave, high current: A Rectangular wave, duty cycle: % Sine/half-sine current amplitude: A Triangle/half-triangle current amplitude: A Custom RMS current: A Custom average rectified current: A MOSFET on-state/resistor resistance: Ω IGBT/Diode voltage drop: V Power dissipation: 0W

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Function list:
• basic calculations (DC power, AC power, LED resistor, Ohm's law, E6/E12/E24 series selector)
• capacitor reactance, inductor reactance, RLC impedance, aperiodicity, resonant frequency calculation
• capacitor dv/dt, maximum current calculation, tan delta to ESR converter
• rise time ↔ bandwidth calculator
• decibel to ratio conversions
• toroid inductance calculator
• capacitor energy and voltage rise
• 555, TL494, UC384x calculator
• MOSFET, IGBT, diode switching and conduction loss calculator