Three Phase RMS Voltage Calculator

Calculator Inputs

Input mode

Connection type

Known voltage value

Voltage unit

Active power

Power unit

Line current

Power factor

Frequency

Phase A angle

Sample type

Sample set A

Sample set B

Sample set C

Example Data Table

Known Input	Connection	Line RMS	Phase RMS	Line Peak	Use Case
415 V line RMS	Star / Wye	415 V	239.6 V	586.9 V	Panel voltage review
480 V line RMS	Delta	480 V	480 V	678.8 V	Motor supply check
100 kW, 160 A, PF 0.9	Star / Wye	400.9 V	231.5 V	567 V	Load estimate

Formula Used

Direct RMS: Vrms = √((v1² + v2² + ... + vn²) / n)

Sine wave RMS: Vrms = Vpeak / √2

Peak-to-peak conversion: Vrms = Vpp / (2 × √2)

Star connection: VLL = √3 × Vphase

Delta connection: VLL = Vphase

Three phase power: P = √3 × VLL × I × PF

Voltage from power: VLL = P / (√3 × I × PF)

How To Use This Calculator

Select the input mode that matches your known data.
Choose star or delta connection type.
Enter voltage, power, current, or waveform samples.
Enter power factor when power calculations are needed.
Add frequency to calculate period and angular frequency.
Press Calculate to show results above the form.
Use CSV or PDF buttons to save the result.

Three Phase RMS Voltage Guide

What This Calculator Does

A three phase RMS voltage calculation turns changing AC voltage into a useful heating equivalent. RMS means root mean square. It lets a sinusoidal waveform be compared with direct voltage. In a balanced system, each phase has the same magnitude. The phases are separated by 120 electrical degrees. That spacing keeps power delivery smooth. It also lowers conductor demand for many loads.

Line And Phase Voltage

Three phase voltage is often stated as line to line RMS voltage. This is the voltage measured between two line conductors. In a star connection, line voltage equals phase voltage times the square root of three. Phase voltage is measured from line to neutral. In a delta connection, line voltage and phase voltage are normally equal. The calculator applies these relationships after it identifies your known input.

Peak And RMS Conversion

Many meters show RMS values. Oscilloscopes may show peak or peak to peak voltage. For a clean sine wave, RMS voltage equals peak voltage divided by square root of two. Peak to peak voltage is twice the peak value. These rules make quick conversion possible. They should not be used for distorted waveforms unless true RMS sampling is used.

Power Based Voltage

Balanced three phase power uses line voltage, line current, and power factor. Real power equals square root of three times line RMS voltage times line current times power factor. This calculator can rearrange that formula. It can estimate voltage from power and current. It can also estimate current or power when the other values are supplied.

Sample Data Mode

Sample mode is useful for logged waveforms. Enter numeric samples for each phase. The tool squares every sample, finds the mean, and then takes the square root. This is the direct RMS definition. It also reports phase average and voltage unbalance. More samples usually give a better result. Use one or more complete cycles when possible.

Practical Use

Use this tool for motor checks, panel planning, transformer review, and lab notes. Always confirm the connection type first. Use safe instruments. Never measure live equipment without training. The calculator supports design review. It does not replace local electrical codes, protective studies, or field testing.

FAQs

What is RMS voltage?

RMS voltage is the effective AC voltage. It gives the same heating effect as an equal DC voltage across a resistive load.

What is line-to-line voltage?

Line-to-line voltage is measured between two phase conductors. It is the common voltage rating used for many three phase systems.

What is phase voltage?

Phase voltage is measured across one phase. In star systems, it is line to neutral. In delta systems, it equals line voltage.

Why does star voltage use square root of three?

The three phase vectors are separated by 120 degrees. Their vector difference creates the square root of three relationship.

Can I use peak voltage as input?

Yes. Select line peak or phase peak mode. The calculator divides the peak value by square root of two.

Can this calculate voltage from power?

Yes. Enter active power, line current, and power factor. The tool rearranges the balanced three phase power formula.

When should I use sample mode?

Use sample mode when you have logged waveform values. It applies the direct root mean square definition to those samples.

Does this replace field testing?

No. It supports planning and checking work. Use proper meters, safe procedures, and qualified judgment for live systems.