Power & Efficiency Formulas
Power and efficiency formulas quantify how much energy a system delivers versus how much it wastes as heat. These calculators evaluate converter efficiency, loss, and dissipation so you can target thermal and battery budgets. They are key to designing supplies that run cool and last long.
Power & Efficiency Formula Calculators
- Linear Regulator Dissipation P = (Vin − Vout) × I Input Voltage 3.3 V, Output Voltage 1.55 V, Load Current 20 mA → Power = 35 mW
- Efficiency η = Pout / Pin Output Power 10 mW, Input Power 22 mW → Efficiency = 45.45 %
- Buck Converter Vout = Vin × D Input Voltage 0.726 V, Duty Cycle 2.5 % → Output Voltage = 18.15 mV
- Boost Converter Vout = Vin / (1 − D) Input Voltage 0.726 V, Duty Cycle 2.5 % → Output Voltage = 0.7446 V
- Peukert Effect t = C / I^k Rated Capacity 0.2 Ah, Discharge Current 2 mA, Peukert Exponent 0.025 → t = 0.2336 h
- Energy After Losses Eout = Ein × η Input Energy 7.92 kJ, Efficiency 2.5 % → Output Energy = 0.198 kJ
- Solar Charge Time t = (Cap × V) / (P × η) Battery Capacity 0.2 Ah, Battery Voltage 0.33 V, Panel Power 10 mW, System Efficiency 2.5 % → Charge Time = 264 h
- LDO Minimum Output Vout_min = Vin − Vdrop Input Voltage 0.726 V, Dropout Voltage 10 mV → Min Output Voltage = 0.716 V
- Buck Converter Input Current Iin = Iout × Vout / (Vin × η) Output Current 4.4 mA, Output Voltage 0.33 V, Input Voltage 0.726 V, Efficiency 2.5 % → Input Current = 80 mA
- SMPS Output Voltage Ripple ΔV = Iout × D × (1−D) / (f × C) Voltage Ripple 10 mV, Output Current 2 mA, Duty Cycle 2.5 %, Switching Frequency 100 Hz → Output Capacitance = 48.75 µF
- SMPS Inductor Current Ripple ΔI = Vin × D / (f × L) Input Voltage 0.33 V, Duty Cycle 2.5 %, Switching Frequency 100 Hz, Inductance 100 nH → Current Ripple = 0.825 kA
- Three-Phase Power P = √3 × VLL × IL × cos(φ) Line-to-Line Voltage 0.33 V, Line Current 2 mA, Power Factor 0.025 → Total Power = 28.58 µW
- Flyback Converter Turns Ratio Np/Ns = Vin×D / (Vout×(1−D)) Input Voltage 0.33 V, Duty Cycle 5.5 %, Output Voltage 0.726 V → Turns Ratio (Np/Ns) = 0.02646
- Charge Pump Output Voltage Vout = N × Vin − N × Vf Multiplier Stage Count 0.025, Input Voltage 0.726 V, Diode Forward Voltage 1.55 V → Output Voltage = -20.6 mV
- Buck-Boost Duty Cycle D = Vout / (Vin + Vout) Output Voltage 0.33 V, Input Voltage 0.726 V → Duty Cycle = 31.25 %
- Forward Converter Output Vout = Vin × D × N2/N1 Input Voltage 0.726 V, Duty Cycle 2.5 %, Secondary Turns 0.055, Primary Turns 0.118 → Output Voltage = 8.46 mV
- SMPS Input Filter Inductor L = Vin / (ΔI × f) Input Voltage 0.33 V, Ripple Current 2 mA, Switching Frequency 100 Hz → Inductance = 1.65 H
- Half-Bridge Dead Time t_dead = Qgd / Igate Gate-Drain Charge 100 pC, Gate Drive Current 2 mA → Dead Time = 50 ns
- PFC Boost Inductor L = Vin² × (Vout − Vin) / (Vout × ΔI × f × Pout) Input Voltage (RMS) 0.33 V, Output Voltage 0.726 V, Max Ripple Current 2 mA, Switching Frequency 100 Hz, Output Power 10 mW → L = 2.97 × 10⁷
- Hold-Up Time Capacitor t = C × (Vmax² − Vmin²) / (2 × P) Bulk Capacitance 100 nF, Max Voltage (charged) 0.33 V, Min Voltage (cutoff) 0.726 V, Load Power 10 mW → Hold-Up Time = -2.091 µs
- Switching Loss (Power Context) Psw = 0.5 × V × I × (tr + tf) × f Drain Voltage 0.33 V, Drain Current 2 mA, Rise Time 100 ps, Fall Time 0.22 ns, Switching Frequency 100 Hz → Switching Loss = 1.06 × 10⁻⁵ µW
- Half-Wave Rectifier DC Output Vdc = Vpeak / π Peak Voltage 0.726 V → Average DC Voltage = 0.2311 V
- Full-Wave Rectifier DC Output Vdc = 2 · Vpeak / π Peak Voltage 0.726 V → Average DC Voltage = 0.4622 V
- Bridge Rectifier Peak Output Vdc = Vpeak − 2 · Vdiode Transformer Peak 0.726 V, Diode Drop 1.55 V → DC Output (peak) = -2.374 V
- Rectifier Ripple Factor r = √((Vrms/Vdc)² − 1) Output RMS Voltage 3.3 V, Output DC Voltage 1.55 V → Ripple Factor = 1.88
- Rectifier Efficiency η = Pdc / Pac DC Output Power 10 mW, AC Input Power 22 mW → Efficiency = 45.45 %
- Peak Inverse Voltage (Centre-Tap) PIV = 2 · Vpeak Peak Voltage 0.726 V → Peak Inverse Voltage = 1.452 V
- Capacitive Dropper Supply Current I = 2π · f · C · Vrms Line Frequency 5 Hz, Dropper Capacitor 100 nF, Line Voltage 0.33 V → Supply Current = 1.037 µA
- Half-Wave Rectified RMS Voltage Vrms = Vpeak / 2 Peak Voltage 0.726 V → RMS Voltage = 0.363 V
- Boost Inductor Value L = Vin·(Vout−Vin) / (ΔIL·fs·Vout) Input Voltage 0.33 V, Output Voltage 0.726 V, Ripple Current 100 µA, Switching Frequency 100 Hz → Inductance = 18 H
- Boost Inductor Ripple Current ΔIL = Vin · D / (fs · L) Input Voltage 0.33 V, Duty Cycle 2.5 %, Switching Frequency 100 Hz, Inductance 100 nH → Ripple Current = 0.825 kA
- Boost Peak Switch Current Ipk = Iout/(1−D) + ΔIL/2 Output Current 4.4 mA, Duty Cycle 2.5 %, Ripple Current 100 µA → Peak Current = 4.563 mA
- Boost Output Capacitor Cout = Iout · D / (fs · ΔVout) Output Current 2 mA, Duty Cycle 2.5 %, Switching Frequency 100 Hz, Output Ripple 10 mV → Output Capacitance = 50 µF
- Buck Output Ripple (with ESR) ΔVout = ΔIL · (ESR + 1/(8·fs·Cout)) Ripple Current 100 µA, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz, Output Capacitance 100 nF → Output Ripple = 1.25 V
- Regulator Feedback Divider Vout = Vref · (1 + R1/R2) Reference Voltage 0.726 V, Top Resistor 100 Ω, Bottom Resistor 0.22 kΩ → Output Voltage = 1.056 V
- LDO Power Dissipation (with Iq) Pd = (Vin − Vout)·Iout + Vin·Iq Input Voltage 0.33 V, Output Voltage 0.726 V, Output Current 100 µA, Quiescent Current 0.22 mA → Power Dissipation = 33 µW
- LDO Efficiency (with Iq) η = Vout·Iout / (Vin·(Iout + Iq)) Output Voltage 0.33 V, Output Current 100 µA, Input Voltage 0.726 V, Quiescent Current 0.22 mA → Efficiency = 14.2 %
Worked result for every Power & Efficiency formula
| Formula | Expression | Worked result |
|---|---|---|
| Linear Regulator Dissipation | P = (Vin − Vout) × I | Input Voltage 3.3 V, Output Voltage 1.55 V, Load Current 20 mA → Power = 35 mW |
| Efficiency | η = Pout / Pin | Output Power 10 mW, Input Power 22 mW → Efficiency = 45.45 % |
| Buck Converter | Vout = Vin × D | Input Voltage 0.726 V, Duty Cycle 2.5 % → Output Voltage = 18.15 mV |
| Boost Converter | Vout = Vin / (1 − D) | Input Voltage 0.726 V, Duty Cycle 2.5 % → Output Voltage = 0.7446 V |
| Peukert Effect | t = C / I^k | Rated Capacity 0.2 Ah, Discharge Current 2 mA, Peukert Exponent 0.025 → t = 0.2336 h |
| Energy After Losses | Eout = Ein × η | Input Energy 7.92 kJ, Efficiency 2.5 % → Output Energy = 0.198 kJ |
| Solar Charge Time | t = (Cap × V) / (P × η) | Battery Capacity 0.2 Ah, Battery Voltage 0.33 V, Panel Power 10 mW, System Efficiency 2.5 % → Charge Time = 264 h |
| LDO Minimum Output | Vout_min = Vin − Vdrop | Input Voltage 0.726 V, Dropout Voltage 10 mV → Min Output Voltage = 0.716 V |
| Buck Converter Input Current | Iin = Iout × Vout / (Vin × η) | Output Current 4.4 mA, Output Voltage 0.33 V, Input Voltage 0.726 V, Efficiency 2.5 % → Input Current = 80 mA |
| SMPS Output Voltage Ripple | ΔV = Iout × D × (1−D) / (f × C) | Voltage Ripple 10 mV, Output Current 2 mA, Duty Cycle 2.5 %, Switching Frequency 100 Hz → Output Capacitance = 48.75 µF |
| SMPS Inductor Current Ripple | ΔI = Vin × D / (f × L) | Input Voltage 0.33 V, Duty Cycle 2.5 %, Switching Frequency 100 Hz, Inductance 100 nH → Current Ripple = 0.825 kA |
| Three-Phase Power | P = √3 × VLL × IL × cos(φ) | Line-to-Line Voltage 0.33 V, Line Current 2 mA, Power Factor 0.025 → Total Power = 28.58 µW |
| Flyback Converter Turns Ratio | Np/Ns = Vin×D / (Vout×(1−D)) | Input Voltage 0.33 V, Duty Cycle 5.5 %, Output Voltage 0.726 V → Turns Ratio (Np/Ns) = 0.02646 |
| Charge Pump Output Voltage | Vout = N × Vin − N × Vf | Multiplier Stage Count 0.025, Input Voltage 0.726 V, Diode Forward Voltage 1.55 V → Output Voltage = -20.6 mV |
| Buck-Boost Duty Cycle | D = Vout / (Vin + Vout) | Output Voltage 0.33 V, Input Voltage 0.726 V → Duty Cycle = 31.25 % |
| Forward Converter Output | Vout = Vin × D × N2/N1 | Input Voltage 0.726 V, Duty Cycle 2.5 %, Secondary Turns 0.055, Primary Turns 0.118 → Output Voltage = 8.46 mV |
| SMPS Input Filter Inductor | L = Vin / (ΔI × f) | Input Voltage 0.33 V, Ripple Current 2 mA, Switching Frequency 100 Hz → Inductance = 1.65 H |
| Half-Bridge Dead Time | t_dead = Qgd / Igate | Gate-Drain Charge 100 pC, Gate Drive Current 2 mA → Dead Time = 50 ns |
| PFC Boost Inductor | L = Vin² × (Vout − Vin) / (Vout × ΔI × f × Pout) | Input Voltage (RMS) 0.33 V, Output Voltage 0.726 V, Max Ripple Current 2 mA, Switching Frequency 100 Hz, Output Power 10 mW → L = 2.97 × 10⁷ |
| Hold-Up Time Capacitor | t = C × (Vmax² − Vmin²) / (2 × P) | Bulk Capacitance 100 nF, Max Voltage (charged) 0.33 V, Min Voltage (cutoff) 0.726 V, Load Power 10 mW → Hold-Up Time = -2.091 µs |
| Switching Loss (Power Context) | Psw = 0.5 × V × I × (tr + tf) × f | Drain Voltage 0.33 V, Drain Current 2 mA, Rise Time 100 ps, Fall Time 0.22 ns, Switching Frequency 100 Hz → Switching Loss = 1.06 × 10⁻⁵ µW |
| Half-Wave Rectifier DC Output | Vdc = Vpeak / π | Peak Voltage 0.726 V → Average DC Voltage = 0.2311 V |
| Full-Wave Rectifier DC Output | Vdc = 2 · Vpeak / π | Peak Voltage 0.726 V → Average DC Voltage = 0.4622 V |
| Bridge Rectifier Peak Output | Vdc = Vpeak − 2 · Vdiode | Transformer Peak 0.726 V, Diode Drop 1.55 V → DC Output (peak) = -2.374 V |
| Rectifier Ripple Factor | r = √((Vrms/Vdc)² − 1) | Output RMS Voltage 3.3 V, Output DC Voltage 1.55 V → Ripple Factor = 1.88 |
| Rectifier Efficiency | η = Pdc / Pac | DC Output Power 10 mW, AC Input Power 22 mW → Efficiency = 45.45 % |
| Peak Inverse Voltage (Centre-Tap) | PIV = 2 · Vpeak | Peak Voltage 0.726 V → Peak Inverse Voltage = 1.452 V |
| Capacitive Dropper Supply Current | I = 2π · f · C · Vrms | Line Frequency 5 Hz, Dropper Capacitor 100 nF, Line Voltage 0.33 V → Supply Current = 1.037 µA |
| Half-Wave Rectified RMS Voltage | Vrms = Vpeak / 2 | Peak Voltage 0.726 V → RMS Voltage = 0.363 V |
| Boost Inductor Value | L = Vin·(Vout−Vin) / (ΔIL·fs·Vout) | Input Voltage 0.33 V, Output Voltage 0.726 V, Ripple Current 100 µA, Switching Frequency 100 Hz → Inductance = 18 H |
| Boost Inductor Ripple Current | ΔIL = Vin · D / (fs · L) | Input Voltage 0.33 V, Duty Cycle 2.5 %, Switching Frequency 100 Hz, Inductance 100 nH → Ripple Current = 0.825 kA |
| Boost Peak Switch Current | Ipk = Iout/(1−D) + ΔIL/2 | Output Current 4.4 mA, Duty Cycle 2.5 %, Ripple Current 100 µA → Peak Current = 4.563 mA |
| Boost Output Capacitor | Cout = Iout · D / (fs · ΔVout) | Output Current 2 mA, Duty Cycle 2.5 %, Switching Frequency 100 Hz, Output Ripple 10 mV → Output Capacitance = 50 µF |
| Buck Output Ripple (with ESR) | ΔVout = ΔIL · (ESR + 1/(8·fs·Cout)) | Ripple Current 100 µA, Capacitor ESR 0.1 mΩ, Switching Frequency 100 Hz, Output Capacitance 100 nF → Output Ripple = 1.25 V |
| Regulator Feedback Divider | Vout = Vref · (1 + R1/R2) | Reference Voltage 0.726 V, Top Resistor 100 Ω, Bottom Resistor 0.22 kΩ → Output Voltage = 1.056 V |
| LDO Power Dissipation (with Iq) | Pd = (Vin − Vout)·Iout + Vin·Iq | Input Voltage 0.33 V, Output Voltage 0.726 V, Output Current 100 µA, Quiescent Current 0.22 mA → Power Dissipation = 33 µW |
| LDO Efficiency (with Iq) | η = Vout·Iout / (Vin·(Iout + Iq)) | Output Voltage 0.33 V, Output Current 100 µA, Input Voltage 0.726 V, Quiescent Current 0.22 mA → Efficiency = 14.2 % |
Variables used across Power & Efficiency formulas
- P — Power dissipated as heat (W)
- Vin — Input voltage (V)
- Vout — Regulated output voltage (V)
- Iload — Load current (A)
- η — Efficiency ratio (0 to 1, dimensionless)
- Pout — Output power delivered to the load (W)
- Pin — Input power consumed from the source (W)
- D — Duty cycle (0 to 1)
- t — Effective runtime in hours (h)
- C — Rated capacity at 1A discharge rate (Ah)
- I — Actual discharge current (A)
- k — Peukert exponent (dimensionless, >1)
- Eout — Usable output energy (Wh)
- Ein — Total input energy (Wh)
- Capacity — Battery capacity (Ah)
- V — Battery nominal voltage (V)
- Ppanel — Solar panel rated power (W)
- Vout_min — Minimum regulated output voltage (V)
- Vdrop — Dropout voltage (V)
- Iin — Average input current (A)
- Iout — Output load current (A)
- ΔV — Peak-to-peak output voltage ripple (V)
- f — Switching frequency (Hz)
- ΔI — Peak-to-peak inductor current ripple (A)
- L — Inductance (H)
- VLL — Line-to-line RMS voltage (V)
- IL — Line current RMS (A)
- cos(φ) — Power factor
- Np/Ns — Primary to secondary turns ratio
- N — Number of multiplier stages
- Vf — Forward voltage drop per diode (V)
- V_out — Output voltage magnitude (V)
- V_in — Input voltage (V)
- N₂ — Secondary winding turns
- N₁ — Primary winding turns
- t_dead — Minimum dead time (s)
- Q_gd — MOSFET gate-drain (Miller) charge (C)
- I_gate — Gate driver sink current (A)
- P_out — Output power (W)
- V_max — DC bus voltage when fully charged (V)
- V_min — Minimum DC bus voltage for regulation (V)
- P_sw — Average switching power loss (W)
- t_r — Turn-on rise time (s)
- t_f — Turn-off fall time (s)
- Vdc — Average DC output voltage (V)
- Vpeak — Peak of the rectified AC (V)
- Vdiode — Forward drop per diode (~0.7–1 V)
- r — Ripple factor (fraction)
- Vrms — Total RMS of the output (DC + ripple) (V)
- Pdc — DC power delivered to the load (W)
- Pac — AC power drawn from the source (W)
- PIV — Peak inverse (reverse) voltage on the diode (V)
- ΔIL — Target peak-to-peak ripple current (A)
- fs — Switching frequency (Hz)
- Ipk — Peak switch/inductor current (A)
- Cout — Output capacitance (F)
- ΔVout — Allowed output ripple (V)
- ESR — Capacitor equivalent series resistance (Ω)
- Vref — Internal reference voltage (V)
- R1 — Resistor from output to feedback (Ω)
- R2 — Resistor from feedback to ground (Ω)
- Pd — Total power dissipated in the LDO (W)
- Iq — Quiescent/ground current (A)
Questions people ask about Power & Efficiency
- Formule de peukert kt — Peukert Effect
- V line v phase — Three-Phase Power
- V line and v phase — Three-Phase Power
- Buck boost duty cycle formula — Buck-Boost Duty Cycle
- Forward converter vo/vin — Forward Converter Output
- Calculated off bridge time — Half-Bridge Dead Time
- Half-wave rectifier output calculator — Half-Wave Rectifier DC Output
- Calculate dc current of fullwave rectifier — Full-Wave Rectifier DC Output
- Capacitive dropper current formula 230v 50hz 3.3uf capacitor 238ma — Capacitive Dropper Supply Current
- Boost average current peak current — Boost Peak Switch Current
- Buck converter output ripple esr capacitance — Buck Output Ripple (with ESR)
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