Watt Formula

May 8, 2026

What Is a Watt?

A watt measures the rate at which energy is converted or used. One watt equals one joule of energy transferred per second (1 W = 1 J/s). The unit is named after James Watt, the Scottish engineer whose improvements to the steam engine helped spark the Industrial Revolution.

In electrical terms, the watt formula connects three fundamental quantities: voltage (\(V\)), current (\(I\)), and power (\(P\)). The underlying relationship is clean and universal–once you see how it branches into different forms, you can size circuits, estimate electric bills, and avoid overloads.

DC Power Formulas

Direct current delivers a steady voltage, so the watt calculation is straightforward. The base formula is:

P = V × I

Where:

\(P\) is power in watts (W)
\(V\) is voltage in volts (V)
\(I\) is current in amperes (A)

Example: A device drawing 5 A from a 120 V supply consumes \(120 \times 5 = 600\) W.

Because Ohm’s law links voltage, current, and resistance (\(R\)), you can substitute and get two alternative watt formulas that need only one measured value and resistance:

Using \(V = I \times R\):

P = I² × R (power from current and resistance)
P = V² / R (power from voltage and resistance)

A heating element with a resistance of 10 Ω carrying 2 A, for instance, dissipates \(2^2 \times 10 = 40\) W.

The calculator above selects the correct watt formula for you. Pick the mode that matches the values you already know–voltage and current, resistance and current, or voltage and resistance–and it returns power instantly.

AC Power: Real, Apparent, and Reactive

In alternating current circuits, voltage and current can be out of phase. The simple product of RMS voltage and RMS current no longer gives true power; it gives apparent power (\(S\)) in volt‑amperes (VA). The portion that performs actual work is real power (\(P\)) in watts, and the unused portion is reactive power (\(Q\)) in volt‑amperes reactive (VAR).

The key watt formula for AC is:

P = V_rms × I_rms × cos φ

where cos φ is the power factor (PF). The phase angle φ comes from the difference between the voltage and current sine waves.

\(S = V_rms × I_rms\) (VA)
\(P = S × PF\) (W)
\(Q = S × sin φ\) (VAR)
\(S^2 = P^2 + Q^2\)

Example: A motor rated at 230 V RMS, drawing 10 A RMS with a power factor of 0.85 has \(P = 230 \times 10 \times 0.85 = 1,955\) W. The apparent power is 2,300 VA, and the reactive power is about 1,214 VAR.

Three‑Phase Power Calculation

Large commercial and industrial systems use three‑phase power. The watt formula for a balanced three‑phase circuit is:

P = √3 × V_L × I_L × PF

Here \(V_L\) is the line‑to‑line voltage and \(I_L\) the line current. The √3 (approximately 1.732) appears because three voltage waveforms are 120° apart.

A 480 V three‑phase motor pulling 15 A per phase with a 0.90 power factor, for example, draws \(1.732 \times 480 \times 15 \times 0.90 = 11,210\) W (about 11.2 kW).

Mechanical Power and Horsepower

Outside the electrical domain, the watt formula extends to motion. Mechanical power is the rate of doing work:

P = F × v (force × velocity)
P = τ × ω (torque × angular velocity)

The link between electrical and mechanical watts comes through the motor: input electrical power, output mechanical power. When comparing motors, you often see horsepower (hp). The exact conversion is:

1 hp = 746 W

Divide watts by 746 to get horsepower. A 3,730‑W motor thus delivers exactly 5 hp.

Using a calculator eliminates conversion errors when switching between electrical formulas, AC modes, or mechanical units. Choose the quantity you know, input the numbers, and read the power directly in watts.

Frequently Asked Questions

What is the basic formula for power in watts?

The fundamental electrical power formula is P = V × I, where P is power in watts, V is voltage in volts, and I is current in amperes. In a resistive DC circuit, Ohm’s law lets you rewrite this as P = I²R or P = V²/R.

How are watts related to joules?

One watt equals exactly one joule of energy transferred per second (1 W = 1 J/s). This relationship applies to all forms of power–electrical, mechanical, or thermal–because the watt is the SI unit of power.

What is the formula for three‑phase power in watts?

For a balanced three‑phase system, total real power is P = √3 × V_L × I_L × PF, where V_L is the line‑to‑line voltage, I_L is the line current, and PF is the power factor. The factor √3 accounts for the phase shifts in three‑phase delivery.

How do you calculate watts from volts and amps in an AC circuit?

In AC circuits, real power (watts) is P = V_rms × I_rms × PF, where PF is the power factor (cosine of the phase angle). Without the power factor, the product gives apparent power in volt‑amperes, not actual usable watts.

Why does the watt formula include a power factor?

A power factor below 1 indicates that voltage and current are out of phase, reducing the true power available to do work. Multiplying by cos φ corrects the apparent power to real power; for example, a PF of 0.8 means only 80% of the apparent power becomes real watts.

What is the watt‑to‑horsepower conversion?

One mechanical horsepower equals exactly 746 watts. To convert watts to horsepower, divide by 746. For instance, a 1,492‑watt motor delivers about 2 horsepower (1,492 ÷ 746 = 2).