kVA to kVAR Calculator
Convert apparent power (kVA) to reactive power (kVAR) or vice versa. Toggle parameters dynamically using power factor constants.
Power Converter (kVA & kVAR)
How to Use the kVA to kVAR Calculator
Converting apparent kilowatts (kVA) to reactive power (kVAR) is simple. Follow these steps to size your ratings:
- 1Enter Apparent Power: Input the value in apparent power (kVA) into the designating field.
- 2Power Factor: Enter the power factor of your system (typically 0.8 to 1.0).
- 3Calculate: Click the "Calculate to kVAR" button to run the conversion.
- 4View Results: Instantly view the equivalent reactive power (kVAR) result on the screen.
How to Convert kVA to kVAR
In electrical engineering, apparent power in kilovolt-amperes (kVA) represents the total grid capacity supplied to a facility, while reactive power in kilovolt-amperes reactive (kVAR) represents the non-working power that oscillates to maintain electromagnetic fields. Power systems designers size reactive power to select shunt capacitor banks and minimize utility PF penalties. Sizing uses the system power factor (PF) to calculate the perpendicular reactive vector.
Real-Life Sizing Scenarios
Scenario 1: Sizing Utility Transformer Reactive Load
A commercial facility draws 500 kVA of apparent power from the grid at a lagging power factor of 0.85. Sizing the circulating reactive power load in kVAR:
sin(φ) = √(1 - 0.85²) = 0.5268
Reactive Power (kVAR) = 500 kVA × 0.5268 = 263.39 kVAR
Scenario 2: Sizing Shunt Capacitors for a Motor Load
An industrial induction motor consumes 150 kVA of apparent power under full load with a low power factor of 0.78. Sizing the reactive compensation required to improve power factor:
sin(φ) = √(1 - 0.78²) = 0.6258
Reactive Power (kVAR) = 150 kVA × 0.6258 = 93.87 kVAR
Step-by-Step Manual Sizing Guide
- 1Identify Apparent Power: Check the system apparent power rating in kilovolt-amperes (kVA).
- 2Determine Power Factor: Settle the system power factor (PF). If unknown, use 0.80.
- 3Calculate Sine Component: Resolve the reactive power multiplier:
sin(φ) = √(1 - PF²). For a 0.80 PF, this factor equals exactly 0.60. - 4Compute Reactive Power: Multiply apparent power by the sine factor:
kVAR = kVA × √(1 - PF²).
kVA to kVAR Conversion Chart
The table below displays apparent power conversions to reactive power (kVAR) equivalents at power factors of 0.80 and 0.90:
| Apparent Power (kVA) | Power Factor (PF) | Sine Multiplier (sin φ) | Reactive Power (kVAR) |
|---|---|---|---|
| 10 kVA | 0.80 | 0.60 | 6.00 kVAR |
| 50 kVA | 0.80 | 0.60 | 30.00 kVAR |
| 100 kVA | 0.80 | 0.60 | 60.00 kVAR |
| 250 kVA | 0.80 | 0.60 | 150.00 kVAR |
| 10 kVA | 0.90 | 0.4359 | 4.36 kVAR |
| 100 kVA | 0.90 | 0.4359 | 43.59 kVAR |
1 kVA to kVAR
Converting a baseline rating of 1 kVA apparent power to reactive power (kVAR) depends on the system power factor. Sizing at a standard power factor of 0.80:
Reactive Factor = √(1 - 0.80²) = 0.60
Reactive Power = 1 kVA × 0.60 = 0.60 kVAR
kW to kVA to kVAR
Active power (kW), apparent power (kVA), and reactive power (kVAR) form the three legs of the electrical power triangle. Sizing relations are defined by system power factor (PF):
kVA = kW ÷ PF
kVAR = √(kVA² - kW²) = kVA × √(1 - PF²)
This workflow allows engineers to estimate reactive load when only mechanical active load ratings are provided.
kVA to VAR
Volt-Amperes Reactive (VAR) represents the basic unit of reactive power, where 1 kVAR is equal to 1,000 VAR. Sizing the VAR rating directly from apparent power in kVA:
VAR = kVA × √(1 - PF²) × 1,000
For a 10 kVA load operating at 0.85 PF lagging, the reactive power is: 10 × √(1 - 0.85²) × 1,000 = 5,268 VAR.
100 kVA to kVAR
A substation transformer capacity of 100 kVA delivers reactive power based on load phase displacement. Sizing at a standard utility power factor of 0.80:
sin(φ) = √(1 - 0.80²) = 0.60
Reactive power = 100 kVA × 0.60 = 60.00 kVAR
kW and kVAR to kVA Calculation
When real working power (kW) and reactive circulating power (kVAR) are both known, apparent capacity in kVA is determined using vector addition:
kVA = √(kW² + kVAR²)
For example, if a plant load uses 80 kW of active power and 60 kVAR of reactive power, the total capacity demand is: √(80² + 60²) = 100 kVA.
How to Find kVAR from kW and kVA
If apparent power (kVA) and active power (kW) are known, the reactive power (kVAR) is found by rearranging the Pythagorean power triangle formula:
kVAR = √(kVA² - kW²)
This calculation allows designers to estimate how much reactive power can be mitigated by shunt capacitor installations.
Frequently Asked Questions (FAQs)
To convert apparent power (kVA) to reactive power (kVAR), you must know the power factor (PF). Apply the formula: kVAR = kVA × √(1 - PF²).
No. kVA represents apparent power, which is the total capacity supplied to the system. kVAR represents reactive power, which is the portion of capacity circulating in windings to sustain magnetic fields without performing active work.
The standard formula to calculate reactive power is: kVAR = kVA × sin(φ), where φ = acos(PF). Sizing this mathematically is: kVAR = kVA × √(1 - PF²).
kVAR represents the instantaneous reactive power flow in the system. kVArh (Kilovolt-Amperes Reactive Hour) measures the total reactive energy consumed or supplied over a period of time (e.g., active hourly billing periods).
50 kVAR represents 50,000 Volt-Amperes Reactive. It is typically the rating of a power factor correction capacitor bank used to supply magnetizing current locally and reduce grid demand.
Apparent capacity is calculated using voltage and current: kVA = (Volts × Amps) ÷ 1,000 for single-phase systems, or kVA = (√3 × Volts × Amps) ÷ 1,000 for three-phase systems.
Only in a purely resistive circuit where the power factor is exactly 1.0. In reactive circuits (having induction motors or electronics), the active power (kW) is always less than the apparent power (kVA): kW = kVA × PF.
2000 kVA (or 2 MVA) indicates the apparent power capacity of a large industrial transformer or commercial standby generator, designed to feed a heavy facility load.
To calculate kVA apparent power from reactive kVAR, use the formula: kVA = kVAR ÷ √(1 - PF²), incorporating the load power factor value.