Root Mean Square (RMS) current, often denoted as **I _{RMS}**, is equal to the value of direct current (DC) that produces the same power dissipation in a resistive load.

Contents

**Calculator**

To find the RMS current enter

- Average Power
- Resistance

(use the drop down menu to select the units).

**Formula**

RMS values are commonly used in AC circuit analysis because they allow us to use equivalent DC values in calculations involving power, voltage, and resistance. In an AC circuit, the formula for RMS current is therefore given by the formula:

**I _{RMS} = √(P_{avg}/R) **

Where:

**P**is the average power in watts (W)_{avg}**I**is the RMS current in Amperes (A)_{RMS}**R**is the resistance in Ohms (Ω)

**Example Calculation**

For an average power value of 10 Watt and 100 ohm resistance, the RMS current is calculated to be 316 mA.

**RMS Current from data**

Use this calculator to find the RMS current for an arbitrary waveform using instantaneous values of current (I1, I2, I3…) over time.

**Peak current to RMS current**

In the formula used for the calculator above, the current is calculated from the average power. This is independent of the waveform.

For a sinusoindal waveform, RMS current is calculated from the peak current using the following formula (or calculator below)

**I _{RMS} = I_{PEAK} / √2**

Where:

**I**is the RMS current (in Amperes, A)._{RMS}**I**is the peak current (also in Amperes), which is the maximum value of the current waveform in the AC circuit._{PEAK}

To find the RMS current, you first determine the peak current (the highest value the current reaches during one cycle of the AC waveform) and then divide it by the square root of 2 (approximately 1.4142).

Using RMS values in AC calculations simplifies the analysis and ensures that results are comparable to those obtained in DC circuits.

**Why use RMS Current**?

In an AC circuit, the current continuously changes direction and magnitude, unlike direct current (DC), which flows steadily in one direction. RMS current is a way to represent the effective or equivalent current in an AC circuit, which produces the same heating effect as a steady DC current.