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

Table of Contents

Table of Contents

**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 V_{RMS} 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**

**V _{RMS} = |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.

**Calculator**

**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(2 πft)**

The RMS voltage is

**V _{RMS} = Vp/(√2)**

**= Vpp/(2√2)**=

*****

*π***Vavg/(2√2)**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

## 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

**V _{RMS} = Vp/(√2)**

**= Vpp/(2√2)**=

*****

*π***Vavg/(2√2)**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

## Half-wave rectified Sine Wave

**Formula**

RMS voltage is

**V _{RMS} = Vp/2**

**= Vpp/4**=

*****

*π***Vavg/2**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

## Full-wave rectified Sine Wave

**Formula**

The time varying waveform is represented as

**y = |Vp*sin(2 πft)**|

RMS voltage is

**V _{RMS} = Vp/(√2)**

**= Vpp/(2√2)**=

*****

*π***Vavg/(2√2)**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

**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

**V _{RMS} = Vp**

**= Vpp/2**=

**Vavg**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

**Triangle Wave**

**Formula**

**y= |2*Vp*frac(ft) – Vp|**

RMS voltage is

**V _{RMS} = Vp/(√3)**

**= Vpp/(2√3)**=

*****

*π***Vavg/(2√3)**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

**Sawtooth Wave**

**Formula**

**y= 2*Vp*frac(ft) – Vp**

RMS voltage is

**V _{RMS} = Vp/(√3)**

**= Vpp/(2√3)**=

*****

*π***Vavg/(2√3)**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

**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

**V _{RMS} = √D*Vp = √D*Vpp/2**

If there’s a DC offset **V _{DC}** , the RMS voltage is

**V _{RMS-DC} = √(V_{DC}^{2} + V_{RMS}^{2})**

**Calculator**

**Phase-to-phase Voltage**

**Formula**

**y = Vp*sin(t) – Vp*sin(t-2π/3)**

**V _{RMS} = Vp*√1.5 = (Vpp/2**)*

**√(1.5)**

**Calculator**

**Frequently Asked Questions**

**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) _{0}∫^{T} 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:

**V**_{RMS} = **√(1/n)(V _{1}^{2} +V_{2}^{2} + … + V_{n}^{2})**

where **V _{1}, V_{2}, … V_{n}** are the corresponding values of voltage. The square of each value is positive and therefore

**will be positive.**

**V**_{RMS}**References**

[1] Root-mean-square on Wikipedia

[2] Duty Cycle on Wikipedia

[3] Continuous Wave on Wikipedia

[4] Modified Sine Wave on Wikipedia