Single-phase power calculator
Active, apparent and reactive power of a single-phase circuit, or current from power.
Fill in the fields and the result will appear here automatically.
Relate RMS voltage U and current I to active, apparent and reactive power of a single-phase sinusoidal load. Find P from I or I from P. This is a steady-state model with PF = cos φ, not a cable, breaker or starting-current calculation. For nonsinusoidal current, measured PF can differ from cos φ and the displayed Q does not describe every non-active component.
How it works
Formula and logic
P = U·I·PF in watts; S = U·I in volt-amperes. The inverse is I = P/(U·PF). In sinusoidal operation, |Q| = S·√((1−PF)(1+PF)). At PF = 1 reactive power is zero; at I = 0 all powers are zero. Voltage must be positive because the inverse mode divides by U.
Example
230 V, 8 A and PF = 0.9 give P = 1 656 W, S = 1 840 VA and |Q| ≈ 802.04 var. The inverse with 1 656 W at the same U and PF returns 8 A. At PF = 1 and 8 A, P = S = 1 840.
Fields and units
- What to find — list option
- RMS voltage — V
- RMS current — A
- Active power — W
- Power factor cos φ — 1
How to use
- — Choose active power or current and fill the visible known-current or known-power field.
- — Enter RMS voltage in V, not the sine-wave amplitude.
- — Use PF greater than 0 and at most 1; known current or power may be zero but cannot be negative.
- — Check units: P in W, S in VA and Q magnitude in var. Protection ratings require a separate calculation.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: average power, RMS values and cos φ
- Limitation
- Single-phase sinusoidal RMS model. Harmonics, Q sign, transients, protection and conductor current limits are not calculated.
FAQ
Is RMS voltage the same as amplitude?
No. For a sine wave, Urms = Upeak/√2, and similarly for current. Entering both peak values instead of RMS makes their product twice as large.
Why do watts, volt-amperes and vars differ?
P is average active power, S is the product of RMS U and I, and Q is the reactive component in the sinusoidal model. They satisfy S² = P² + Q², not S = P + Q.
Can the result select a cable or breaker?
Current alone is insufficient. Installation, heating, length, starting behaviour, protection and applicable rules also matter. Those inputs are absent, so this page does not produce a design decision.
What does a zero or negative load mean?
Zero known current or power gives an algebraic no-consumption case. Negative values are rejected because this model uses passive-load magnitudes, not signed generator energy flow. PF = 0 is excluded because of inverse division.