SpecCalc Hub
kW, kVA & kVAr Calculator: Power Factor Triangle
Relate active, apparent and reactive power using the selected inputs. kVAr is power; kVArh is accumulated reactive energy.
Preliminary estimate only. Not a code-compliance document, not installation approval, not final engineering design. Verify with qualified professional and local codes.
Enter the values
Client-side estimate. SpecCalc Hub does not store entered values.
Formula: S^2 = P^2 + Q^2; PF = P / S
Reference formula
This simplified formula block is educational and depends on the page status and limitations.
S^2 = P^2 + Q^2; PF = P / S
Assumptions
- Inputs are user-provided.
- The result is an informational estimate.
Limitations
- Professional verification is required before real-world use.
What this page helps with
Relate active, apparent and reactive power using the selected inputs. kVAr is power; kVArh is accumulated reactive energy.
Complete a sinusoidal power triangle from the selected pair of known quantities. Only the fields for that mode participate in validation and calculation.
Formula or method
For the sinusoidal power-triangle model: S² = P² + Q², PF = P / S and Q = P × tan(arccos(PF)). Choose the input pair you actually know; no universal constant converts kW to kVAr.
The working method on this page uses inputs such as Known values, kW, kVA, and kVAr and reports outputs such as Real power, Apparent power, and Reactive power. The formula, assumptions and limitations stay visible so the result can be reviewed instead of simply trusted.
This makes the page useful for comparison and documentation, but it does not automatically include every manufacturer coefficient, installation condition, environmental factor or local-code requirement that may matter in a real project.
How to use
- Enter the page inputs, starting with Known values, and confirm that the units match the real scenario you are checking.
- Read the main output Real power together with the other reported values instead of focusing on only one number.
- Before a real decision, review the assumptions, limitations, source links and related tools on the same page.
Practical examples
A common question, worked through
At P = 10 kW and PF = 0.8, S = 12.5 kVA and Q = 7.5 kVAr. Constant 7.5 kVAr over two hours corresponds to 15 kVArh, but meter billing rules are a separate subject.
Worked example with the form defaults
Example inputs: Known values: kW + PF; kW: 10 kW; Power factor: 0.85. S^2 = P^2 + Q^2; PF = P / S. Calculated outputs: Real power: 10 kW; Apparent power: 11.765 kVA; Reactive power: 6.197 kVAr; Power factor: 0.85.
Common mistakes
- Using the page without checking units, document revision or the real operating context.
- Treating a preliminary result or reference table as a final engineering decision.
- Ignoring the source links, limitations and related tools needed for the next validation step.
Limitations
- A basic triangle does not fully model harmonic distortion. A reactive-energy meter reading is not an instantaneous kVAr input; capacitor-bank design also needs harmonic, switching and resonance checks.
- The model uses the magnitude of reactive power and does not represent harmonic distortion or distinguish leading from lagging loads. A zero-power state has no defined power factor.
- Professional verification is required before real-world use.
- The page does not replace official manufacturer documentation, local rules or site measurements.
- Separate professional verification is required for safety, protection, cable or installation decisions.
FAQ
Why is power factor required for kW-to-kVAr?
The same active power can occur with different reactive powers. Power factor or another independent quantity is needed to determine the triangle.
Are kVAr and kVArh interchangeable?
No. kVAr describes reactive power; kVArh accumulates reactive energy over time. A constant 7.5 kVAr for two hours corresponds to 15 kVArh, not a new 15 kVAr load.
Does the power triangle model cover all distorted waveforms?
No. The simple triangle is a sinusoidal planning model. Harmonics and true power factor can require a more detailed measured analysis; do not size correction equipment from this estimate alone.
Related tools
Explanation updated: 2026-09-16
Graphics
This calculator provides an estimate for informational purposes only. It is not a certified engineering design, electrical safety approval, or professional installation recommendation. Always verify final decisions with a qualified professional and applicable local codes.