RMS Voltage with DC Offset Calculator

This post features a series of calculators to find the Root-mean-square (RMS) voltage with DC offset of different waveforms.

How to Calculate RMS Voltage

To use the calculators below, use the drop down menu to specify one of the following:

• Peak Voltage – Vp
• Peak-to-peak Voltage – Vpp
• Average Voltage – Vavg

The units of VRMS are the same as those of the input voltage.

Time domain samples

Calculate the RMS value using any number of time domain samples. These samples can be used to specify an arbitrary waveform.

DC

Direct current is a signal level that has a fixed value and does not vary with time. The RMS voltage in this case is the same as the peak voltage. Since there is no variation, the peak to peak and average values are also the same.

Formula

VRMS = |Vp|

A DC/fixed value can also be entered into the time-domain sample RMS calculator to confirm this.

DC is shown in the picture above (red line) relative to other signal types.

Sine Wave

This is one of the most common waveforms used in RF engineering labs. Also known as a continuous wave (CW) signal. The default output from an RF signal generator is a sine wave. It is used to test various RF components such as amplifiers, filters and splitters.

Formula

The time varying sinusoidal waveform is

y = Vp*sin(2πft)

The RMS voltage is

VRMS = Vp/(√2) = Vpp/(2√2) = π*Vavg/(2√2)

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Modified Sine Wave

This is the sum of two square waves, one of which is delayed 0.25 of a period relative to the other.

Formula

The time varying signal is given by the following equations:

y = 0, frac(ft) < 0.25

y = Vp, 0.25 < frac(ft) < 0.50

y = 0, 0.50 < frac(ft) < 0.75

y = -Vp, 0.75 < frac(ft) < 1

The RMS voltage is

VRMS = Vp/(√2) = Vpp/(2√2) = π*Vavg/(2√2)

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Half-wave rectified Sine Wave

Formula

RMS voltage is

VRMS = Vp/2 = Vpp/4 = π*Vavg/2

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Full-wave rectified Sine Wave

Formula

The time varying waveform is represented as

y = |Vp*sin(2πft)|

RMS voltage is

VRMS = Vp/(√2) = Vpp/(2√2) = π*Vavg/(2√2)

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Square Wave

Formula

The time varying signal is given by the following equations:

y = Vp, frac(ft) < 0.50

y = -Vp, frac(ft) > 0.50

RMS voltage is

VRMS = Vp = Vpp/2 = Vavg

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Triangle Wave

Formula

y= |2*Vp*frac(ft) – Vp|

RMS voltage is

VRMS = Vp/(√3) = Vpp/(2√3) = π*Vavg/(2√3)

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Sawtooth Wave

Formula

y= 2*Vp*frac(ft) – Vp

RMS voltage is

VRMS = Vp/(√3) = Vpp/(2√3) = π*Vavg/(2√3)

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Pulse Wave

Formula

The time varying signal is given by the following equations:

y = Vp, frac(ft) < D

y = 0, frac(ft) > D

Where D is the duty cycle expressed as a percentage (%).

RMS voltage is

VRMS = √D*Vp = √D*Vpp/2

If there’s a DC offset VDC , the RMS voltage is

VRMS-DC = √(VDC2 + VRMS2)

Phase-to-phase Voltage

Formula

y = Vp*sin(t) – Vp*sin(t-2π/3)

VRMS = Vp*√1.5 = (Vpp/2)*√(1.5)

What is VRMS?

VRMS stands for “Voltage Root Mean Square.” It is a measure of the root mean square value of an alternating current (AC) or voltage signal.

VRMS is used in electrical engineering and physics to describe the equivalent steady-state DC (direct current) voltage that would produce the same heating effect in a resistive electrical circuit as the AC voltage being measured.

In AC circuits, the voltage or current is constantly changing in magnitude and direction over time, typically following a sinusoidal waveform. VRMS is calculated by taking the square root of the mean (average) of the squares of the instantaneous values of voltage over one complete cycle of the AC waveform. This calculation results in a value that represents the effective or equivalent DC voltage that would produce the same power or heating effect in a resistive component (like a resistor) as the AC voltage in the circuit.

Mathematically, VRMS can be expressed as:

VRMS = √[(1/T) 0T V(t)2 dt]

Where:

• VRMS is the root mean square voltage.
• T is the period of the AC waveform (the time it takes to complete one full cycle).
• V(t) represents the instantaneous voltage at time t during one cycle.

Note that VRMS then depends on the waveform V(t). The calculators on this page have taken this into account and use closed-form expressions to calculate values for Sine, Triangle, Square wave and other waveform types.

VRMS is a useful measure because it allows us to compare AC voltages to DC voltages on an equivalent basis, especially when calculating power or heat dissipation in resistive components in AC circuits.

It is commonly used in electrical engineering to determine the effective voltage or current values in AC circuits for various applications, including power distribution, electronics, and electrical systems analysis.

Is the RMS voltage a positive or negative number?

The Root mean square value of voltage is always a positive number. Note the definition given by the formula:

VRMS = √(1/n)(V12 +V22 + … + Vn2)

where V1, V2, … Vn are the corresponding values of voltage. The square of each value is positive and therefore VRMS will be positive.

References

[1] Root-mean-square on Wikipedia

[2] Duty Cycle on Wikipedia

[3] Continuous Wave on Wikipedia

[4] Modified Sine Wave on Wikipedia