Three Phase kVA Calculator: Formula and Examples

A three-phase kVA calculator estimates apparent power from line voltage and line current using the three-phase power formula. Enter voltage in volts and current in amperes to get kVA; the result is an electrical calculation, not a recommendation for equipment or wiring size.

Formula

For a balanced three-phase system, apparent power is S = √3 × V_L × I_L. In kilovolt-amperes, divide the volt-ampere result by 1,000: kVA = √3 × V_L × I_L ÷ 1,000.

• S is apparent power in volt-amperes (VA).
• V_L is line-to-line voltage in volts (V), measured between two phase conductors.
• I_L is line current in amperes (A), measured in one phase conductor.
• √3 is approximately 1.732, the factor used for a balanced three-phase system.

The calculator’s first output is kVA, the requested quantity. Its second output converts that result to VA. The formula applies to balanced three-phase quantities; if the phases carry substantially different currents or voltages, a single line-voltage and line-current pair may not represent total system apparent power accurately.

Worked Example

Using the calculator defaults, the line-to-line voltage is 400 V and the line current is 10 A.

1. Multiply voltage by current: 400 × 10 = 4,000 VA before applying the three-phase factor.
2. Multiply by √3: 1.73205 × 4,000 ≈ 6,928.2 VA.
3. Convert VA to kVA: 6,928.2 ÷ 1,000 ≈ 6.93 kVA.
4. As a cross-check, 6.93 kVA × 1,000 is about 6,928 VA when rounded to a whole VA.

The displayed kVA is rounded to two decimal places. Small differences in the last digit can result from using a rounded value of √3.

What kVA Means in Three-Phase Power

kVA measures apparent power: the combined electrical demand represented by voltage and current, without accounting for how effectively that current produces useful real power. Real power is commonly expressed in kilowatts (kW). In an AC system, the relationship is kW = kVA × power factor, when the power factor is expressed as a decimal.

For example, a hypothetical 10 kVA load at a power factor of 0.8 corresponds to 8 kW of real power. The calculator does not ask for power factor because it calculates kVA, not kW. Do not treat the two units as interchangeable unless the power factor is known to be 1.0.

Three-phase power is common where larger or more evenly distributed electrical loads are involved. The three conductors carry alternating currents whose phases are separated in time. For a balanced system, the √3 relationship lets you calculate total apparent power using line-to-line voltage and line current rather than calculating each phase separately.

When to Use the Calculator

Use it for a quick mathematical estimate when you know a three-phase system’s line-to-line voltage and line current and want apparent power in kVA. It can help interpret equipment data, compare stated power quantities, or check a calculation. The inputs should describe the same operating condition: pairing a voltage from one point or operating state with a current from another can produce a misleading result.

Check how the data is specified before entering it. Three-phase systems may also be described using phase-to-neutral voltage, phase current, or per-phase power. This calculator specifically expects line-to-line voltage and line current. If a source provides phase-to-neutral voltage instead, do not enter it as though it were line voltage. In a balanced star (wye) system, line-to-line voltage is √3 times phase-to-neutral voltage; relationships for current also depend on whether the connection is star or delta.

Common Mistakes and Limits

• Mixing units: Enter volts, not kilovolts, and amperes, not milliamperes. For instance, 0.4 kV must be converted to 400 V before entry.
• Using phase voltage by mistake: The formula uses line-to-line voltage. Confirm whether a listed voltage is between phases or from phase to neutral.
• Omitting √3: Multiplying voltage and current alone gives a single-phase-style VA product, not the balanced three-phase result.
• Confusing kVA with kW: Convert to real power only when the relevant power factor is available.
• Overinterpreting rounded data: The output is rounded to two decimal places. Meter accuracy, changing loads, and input rounding can matter more than the final displayed digit.

The simple expression assumes balanced conditions and suitable RMS AC voltage and current values. With unbalanced phases, harmonics, or changing loads, total power may require phase-by-phase measurements and a method appropriate to the system. The calculator cannot determine the cause of an abnormal reading, predict energy use, or establish what capacity an installation needs.

Using kVA for Equipment Decisions

kVA is often used to state the apparent-power capacity of electrical equipment, but this calculated number alone does not determine whether a particular supply, generator, transformer, or load is suitable. Actual operating conditions, starting currents, load variation, power factor, voltage, frequency, phase balance, and manufacturer specifications may all matter. A result is a general calculation, not a safety assessment or equipment-sizing instruction.

For design, installation, or troubleshooting, have a qualified electrical professional evaluate the complete system and applicable equipment documentation. Do not select conductors, protective devices, or equipment solely from this calculator’s kVA result.

Frequently Asked Questions

What is the formula for three-phase kVA?
For a balanced three-phase system, kVA = √3 × line-to-line voltage in volts × line current in amperes ÷ 1,000.

Why is √3 used in the calculation?
In a balanced three-phase system, the relationship between the phase quantities and line quantities produces the √3 factor when total apparent power is calculated from line-to-line voltage and line current.

Can I calculate kW from three-phase kVA?
Only if you also know the power factor. Multiply kVA by power factor as a decimal to estimate kW; for example, 10 kVA at 0.8 power factor is 8 kW.

Does this calculator work for single-phase power?
No. It uses the balanced three-phase formula. Single-phase apparent power is voltage multiplied by current, with units converted as needed.

What if the phase currents are unbalanced?
A single line-current value may not describe the total accurately. Use appropriate measurements for each phase and have the system assessed using a method suited to its conditions.

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in v | Line voltage | V | 400 | 0 | 1000000
in i | Line current | A | 10 | 0 | 1000000
out kva | Apparent power | kVA | sqrt(3) * v * i / 1000 | 2
out va | Apparent power | VA | kva * 1000 | 0