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Watts (Power)

Reference entry · last updated 20260908

Watts measure power, the rate of energy transfer or conversion. One watt (W) equals one joule per second. The unit applies to electrical, mechanical, and thermal power.[1]

1. First principles and definitions

Energy is an amount; power describes how fast that amount changes. A device drawing a constant 10 W converts 10 J of electrical energy each second.[2]

\[1\,\mathrm{W}=1\,\mathrm{J/s}\]

2. Electrical power

For steady DC, multiply voltage across a device by current through it. Volts measure energy per charge; amps measure charge per second. Their product gives energy per second.[2]

\[P=VI\]

Illustrative calculation: a device drawing 2 A at 12 V consumes 24 W. At 24 V, a device consuming the same 24 W draws 1 A. These calculations assume steady DC at the device terminals.

3. AC power and volt-amperes

Instantaneous power is voltage times current at the same instant. For sinusoidal AC, average real power is root-mean-square (RMS) voltage times RMS current times the cosine of their phase difference, φ. That cosine is the power factor for sinusoidal waveforms.[3]

\[P_{\mathrm{avg}}=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\varphi\]

The RMS voltage-current product is apparent power, expressed in volt-amperes (VA). It equals real power in watts when the power factor is 1. Illustrative calculation: 230 V RMS × 2 A RMS gives 460 VA; at a power factor of 0.8, real power is 368 W.[5]

4. Watts and watt-hours

A watt-hour (Wh) measures energy. At constant power, energy in Wh equals power in W multiplied by time in hours. One kilowatt is 1,000 W; one kilowatt-hour is 1,000 Wh.[4]

\[E=P\,t\]

Illustrative calculation: a 100 W device running for 3 hours uses 300 Wh, or 0.3 kWh. One watt-hour equals 3,600 J. For changing power, energy is the integral of power over time.[2]

5. See also

6. References

  1. NIST, The Two Classes of SI Units and the SI Prefixes, Tables 1 and 3
  2. OpenStax, University Physics Volume 2, §9.5: Electrical Energy and Power (2016)
  3. OpenStax, University Physics Volume 2, §15.4: Power in an AC Circuit (2016)
  4. U.S. Energy Information Administration, Measuring electricity
  5. Fluke, 43B Applications Manual, chapter 7, pp. 75 and 77: Apparent Power and Power Factor (PDF)