How to Calculate Electrical Power
Electrical power, just like mechanical power, is the amount of work performed in a unit of time. In electrical circuits, work is performed by an electric current. The power depends on the "amount of workers available in a unit of time" — the current I and the energy of "a single worker" — the voltage V.
DC Circuit Power Formula
In a DC (Direct Current) circuit, the power is:
P = I × V
- I [A] — Current in amperes
- V [V] — Voltage in volts
- P [W] — Power in watts
AC Circuit Power Formula
In AC (Alternating Current) circuits, the equation includes the power factor:
P = I × V × pf
where pf stands for power factor.
What Is the Power Factor?
In AC currents, both the current and voltage vary periodically in time. The values I or V correspond to the root mean square (RMS) values.
RMS is the square root of the mean of squares of numbers. The commonly referred voltage of electrical outlets — 230 V in the EU and Australia, 120 V in the USA and Canada, 100 V in Japan — is the RMS voltage.
In AC circuits, the current and voltage might not be in phase. The maximum value of the current might be ahead of or lag behind the maximum value of the voltage. This makes the transfer of power less effective. In the worst case, when the current and voltage are entirely out of sync, the transmitted power is zero.
The power factor tells us how synchronized the current is with the voltage:
- If they're in sync, the power factor is 1 (purely resistive load)
- Otherwise, it is less than one
- In the completely out-of-sync case, it reaches 0
The power factor depends on the device. For a device that is purely resistive, like an electric kettle or an electric heater, the power factor is 1. A device with inductive or capacitive elements puts the current and voltage out of phase, making its power factor less than 1.
AC Power Components
In AC circuits, there are three types of power that form a power triangle:
- Real Power (P) in watts (W) — the actual power consumed by the device: P = I × V × pf
- Apparent Power (S) in volt-amperes (VA) — the product of RMS current and voltage: S = I × V
- Reactive Power (Q) in volt-amperes reactive (VAR) — power stored and released by inductors/capacitors
Unit Conversions
This calculator provides results in both metric and American unit systems:
Metric Units
- Watts (W) — the SI base unit of power
- Kilowatts (kW) — 1 kW = 1,000 W
- Megawatts (MW) — 1 MW = 1,000,000 W
American Units
- Horsepower (HP) — 1 HP = 745.7 W (mechanical horsepower)
- BTU per hour (BTU/hr) — 1 W = 3.41214 BTU/hr
Electricity Cost Calculation
The calculator can also estimate electricity costs. Enter the daily usage hours and the electricity rate (cost per kWh) to see your daily, monthly (30 days), and yearly (365 days) electricity cost. Supported currencies include USD ($), RUB (₽), EUR (€), GBP (£), JPY (¥), CNY (¥), INR (₹), and BRL (R$).
FAQs
What is electrical power?
Electrical power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.
How do I calculate power from current and voltage?
For a DC circuit: multiply the current (in amperes) by the voltage (in volts). The result is power in watts. For an AC circuit: also multiply by the power factor.
What is a typical power factor?
Pure resistive loads (heaters, incandescent bulbs) have pf = 1. Motors and fluorescent lights typically have pf between 0.7 and 0.9. Power companies often require large consumers to maintain pf above 0.9.
What is the difference between watts (W) and volt-amperes (VA)?
Watts (W) measure real power — the energy actually consumed. Volt-amperes (VA) measure apparent power — the total electrical load on the circuit. They are equal only when the power factor equals 1 (pure resistive load).
How many watts is one horsepower?
1 mechanical horsepower (HP) = 745.7 watts. This is the most commonly used conversion. Electrical HP = 746 W; metric HP = 735.5 W.