- Ohm's law
- Power, voltage, current (for DC circuits)
- Voltage, current, phase angle to power (for AC circuits)
- Find a suitable part from the E6/E12/E24-series
- LED resistor calculator
- 3-digit code to capacitance

- Capacitor reactance
- Inductor reactance
- Parallel/series RLC impedance
- LC resonant frequency
- Critical damping (aperiodic) resistance for RLC circuit, LC characteristic impedance

- Inductor DC current rise
- Toroid inductance/turns
- Inductance/turns, general
- Gapped or ungapped inductor/transformer saturation current & inductance

- Capacitor DC voltage rise
- Parallel plate capacitance
- Capacitor charge through resistor - voltage, time
- Capacitor discharge through resistor - voltage, time
- Capacitor stored energy
- Tan δ (loss tangent) ↔ ESR
- Capacitor max. dv/dt, capacitance ↔ max. current
- Capacitive dropper - average rectified current
- Electrolytic, hybrid & polymer capacitor lifespan estimation

- Two transistor astable multivibrator
- 555 astable frequency/duty cycle
- 555 monostable period
- IR2153/IR21531 frequency
- UC384x frequency
- TL494/KA7500 frequency
- Voltage regulator/stabilizer/converter (e.g. LM317T, MC34063) feedback calculations

- IGBT, MOSFET, diode switching power loss (using E)
- MOSFET switching power loss (using tr, tf)
- IGBT, MOSFET gate driver required power consumption
- IGBT, MOSFET, diode, resistor conduction loss

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} |
10^{0} |
10^{3} |
10^{6} |
10^{9} |
10^{12} |
10^{15} |

For convenience, u is used instead of μ.

$P = V \cdot I \cdot \mathrm{cos}(\phi)$

$Q = V \cdot I \cdot \mathrm{cos}(\phi)$

$ |S| = V_{rms} \cdot I_{rms}$

Allowable range: 10pF to 99mF (although capacitors bigger than 10uF usually aren't marked this way)

Tolerance letter | B | C | D | F | G | J | K | M | Z |

Tolerance value | ±0.1pF | ±0.25pF | ±0.5pF | ±1% | ±2% | ±5% | ±10% | ±20% | +80, -20% |

$X_C = \dfrac{1}{2 \cdot \mathrm{\pi} \cdot f \cdot C}$

$X_L = 2 \cdot \mathrm{\pi} \cdot f \cdot L$

$X_C = \dfrac{1}{2 \cdot \mathrm{\pi} \cdot f \cdot C}$

$Z = R + j \cdot 2 \cdot \mathrm{\pi} \cdot f \cdot L - \dfrac{j}{2 \cdot \mathrm{\pi} \cdot f \cdot C}$

$|Z| = \sqrt{R^2+(X_L-X_C)^2}$

If $X_L > X_C$, then $\varphi_i = -\mathrm{arccos} (\dfrac{R}{|Z|})$

If $X_L < X_C$, then $\varphi_i = \mathrm{arccos} (\dfrac{R}{|Z|})$

$|Z| = \dfrac{1}{\sqrt{\frac{1}{R^2} + (\frac{1}{X_L}-\frac{1}{X_C})^2}}$

$\varphi_i = -\mathrm{arctan} (\dfrac{R}{\frac{1}{\frac{1}{X_L} - \frac{1}{X_C}}})$

$f_r = \dfrac{1}{2 \cdot \mathrm{\pi} \cdot \sqrt{ L \cdot C}}$

$Q < 0.5$ ($Q=\dfrac{R}{Z_0}$ for parallel circuit, $Q=\dfrac{Z_0}{R}$ for series circuit, $Z_0 = \sqrt{\dfrac{L}{C}}$)

$I_{max}=C \cdot {\mathrm{max}(\dfrac{\mathrm{d}v(t)}{\mathrm{d}t})}$

This calculator assumes a sine wave input + a constant DC load voltage. For reasonable accuracy, set the limiting resistor value to ≤1/10 of X_{C} at the selected frequency.

Using the resistance calculated through the classic X_{C} calculation to calculate the current gives the RMS current value, not the average rectified value, will give inaccurate current & power (~10% error) with a constant voltage load.

The equation was obtained by integrating the average current (i(t)=C*dv/dt) using a "cut" sine wave according to the voltages, and was verified using LTspice.

This calculator uses the "10-degree rule" (doubling the lifetime with every 10°C temperature drop - compared to the lifetime at the rated max. temperature given the specified ripple current and voltage - k_{1}=2, k_{2}=10) for "classic" liquid electrolytic/hybrid capacitors and the "20-degree rule" (10 times the life with a 20°C temperature drop - k_{1}=10, k_{2}=20).

The estimation won't be particularly accurate at temperatures under 40°C. Also, the lifespan will be much lower at higher currents than specified, at lower currents, it will be higher - refer to manufacturer normograms/datasheets/app-notes for such cases, or the paragraph below.

Optional input - Alternatively, ΔT_{C-norm} (core self-heating over ambient temperature at rated current, depends on exact capacitor, can be about 5-20 degrees), the rated RMS current at the specified frequency, and the actual load current can be used to calculate lifespan at different currents.

The equations and results were checked against application notes and datasheets provided by big capacitor manufacturers such as Rubycon, TDK or Capxon and were found to be reasonably accurate and universal. No endorsement of this calculator by any of these companies is implied. This calculator should be used as a reference, for guaranteed values, check data provided by the manufacturer.

$life_{actual} = life_{rated} \cdot {k_{1}^{\Bigl(\dfrac{T_{A-rated}-T_{A-actual}}{k_2}\Bigr)}} \\[1.2em] \textrm {or: } life_{actual} = life_{rated} \cdot {k_{1}^ {\Bigl(\dfrac{T_{A-rated}-T_{A-actual} + \Delta T_{C-norm} \cdot (1 - (\frac{I_{actual}}{I_{rated}})^2) }{k_2}\Bigr) } } $$\mathrm{max} \dfrac{\mathrm{d}v(t)}{\mathrm{d}t} = 2 \cdot \mathrm{\pi} \cdot f \cdot V_m$

$V_{pk} = \sqrt{2} \cdot V_{rms}$

$t_r = \dfrac{0.35}{BW} \mathrm{(RZ)}, t_r = \dfrac{0.7}{BW} \mathrm{(NRZ)}$

$\mathrm{ratio (dB)} = 10 \cdot \mathrm{lg(ratio)}$

$\mathrm{ratio (dB)} = 20 \cdot \mathrm{lg(ratio)}$

$P = 10^{(0.1 \cdot ({P_{dBm}-30}))}$

For more complex/universal calculations with more possible parameters, use "Gapped or ungapped inductor/transformer saturation current & inductance".

$L = \dfrac{\mu_r \cdot \mathrm{\mu_0} \cdot N^2 \cdot S}{\mathrm{\pi} \cdot d}$

This calculator assumes a reasonably high μ and a closed magnetic circuit.

For more complex/universal calculations with more possible parameters, use "Gapped or ungapped inductor/transformer saturation current & inductance".

$L = \dfrac{N^2 \cdot S \cdot \mathrm{\mu_0} \cdot \mathrm{\mu_r}}{l}$

$R_{m1} = \dfrac{l_{1}}{\mu_0 \cdot \mu_{r1} \cdot S}$, $R_{m2} = \dfrac{l_{2}}{\mu_0 \cdot \mu_{r2} \cdot S}$, $R_{m(tot)} = R_{m1}+R_{m2} \\[0.5em]$ $l_{(tot)} = l_1 + l_2$, $\mu_{eff} = \dfrac{l_{(tot)}}{S \cdot R_{m(tot)}}$ $\\[0.5em]$ $L = \dfrac{N^2}{R_{m(tot)}}$, $I_{sat} = \dfrac{l_{(tot)} \cdot B_{max}}{N \cdot \mu_{eff}}$ $\\[0.5em]$ $F_m = N \cdot I$, $\Phi=\dfrac{F_m}{R_{m(tot)}}=B \cdot S$, $L = \dfrac{\Phi}{I}$, $B = \mu \cdot H$, $H = \dfrac{N \cdot I}{l}$ $\\[0.5em]$

$C = \dfrac{S \cdot \epsilon_r \cdot \mathrm{\epsilon_0} }{l}$

$\tau = R \cdot C$

$t_{total} = \tau \cdot \mathrm{ln} (\dfrac{V_{supply} - V_{initial}}{V_{supply} - V_{final}})$

$V_{final} = V_{initial} + (V_{supply} - V_{initial}) \cdot (1-e^{-t/\tau})$

$\tau = R \cdot C$

$V_{final} = V_{initial} \cdot (1-e^{-t/\tau})$

$E = 0.5 \cdot C \cdot V^2$

$ESR = X_C \cdot \mathrm{tan}( \delta)$

$\tau_2 = R_3 \cdot C_2$

$t_1 = \tau_1 \cdot \mathrm{ln} (\dfrac{2 V_{CC}}{V_{CC}-V_{BE_{sat}}})$

$t_2 = \tau_1 \cdot \mathrm{ln} (\dfrac{2 V_{CC}}{V_{CC}-V_{BE_{sat}}})$

$f=\dfrac{1}{t_1 + t_2}$

$V_{ctrl}$ $=$ 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)

$T = T_{low} + T_{high}$

$f = \dfrac{1}{T}$

$\mathrm{Duty} (\%) = 100\cdot \dfrac{T_{high}}{T}$

$T = -\mathrm{ln}(1-V_{ctrl}) \cdot R \cdot C$

$f_{osc} \approx \dfrac{1.8}{R_t \cdot C_t}$

$V_{out} = V_{ref} \cdot (\dfrac{R2}{R1}+1)$

Chip | Voltage |

LM317T | 1.25V |

MC34063 | 1.25V |

LM2576-ADJ | 1.23V |

LM2596-ADJ | 1.23V |

UC384x (V_{FB}) | 2.5V |

The "scaling factor" K

$P_{sw} = f \cdot E_{ref} \cdot (\dfrac{I}{I_{ref}})^{K_I} \cdot (\dfrac{V}{V_{ref}})^{K_V} \cdot (1 + K_T \cdot (T-T_{ref})) \cdot K_S$

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 (t

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.

$K_g = \dfrac{R_{g\_{int}}+R_{g\_{ext}}}{R_{g\_{int}}+R_{{g\_{ext}}\_{ref}}}$

$E_{cap} = 0.5 \cdot C_{oss} \cdot {V^2_{ds\_{off}}}$

${E_{sw}}_{on} = K_c \cdot K_g \cdot K_l \cdot t_r \cdot {V_{ds\_on}} \cdot {I_{d\_on}}$

${E_{sw}}_{off} = K_c \cdot K_g \cdot K_l \cdot t_f \cdot {V_{ds\_off}} \cdot {I_{d\_off}}$

$P_{sw} = f*({E_{sw\_on}}+{E_{sw\_off}}+E_{cap})$

For simplicity, constant voltage drop + already rectified signal is assumed for diodes, constant resistance is assumed for MOSFETs.

${P_{D,IGBT}} \approx V_{drop} \cdot I_{ARV}$

$P_{MOSFET} \approx R \cdot I^2_{RMS}$

Multiply RMS value of sine/triangle by sqrt(2) to get RMS value of half-rectified sine/triangle

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 | $\sqrt{D \cdot I_{high}^2 +(1-D)\cdot I_{low}^2}$ | $D \cdot I_{high} \\+ (1-D) \cdot I_{low}$ |

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Function list:

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
- multivibrator, 555, TL494, UC384x frequency calculator
- MOSFET, IGBT, diode switching and conduction loss calculator
- capacitive dropper current & power calculator
- ungapped & gapped inductor/transformer calculator, saturation current and inductance calculation
- capacitor (electrolytic, polymer, hybrid) lifespan calculator
- MOSFET/IGBT gate drive circuit power calculator
- voltage regulator resistive divider calculator