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RMS Voltage & Current Calculator

Convert peak AC values to RMS and compute average power

Parameters

Vⓘ
Aⓘ
Show Trail

Controls

xⓘ

Calculated Values

RMS Voltage:
120.21;V120.21;V
RMS Current:
0.71;A0.71;A
Average Power:
85.00;W85.00;W

Examples

170 V peak

~120 V RMS US line.

  • RMS Voltage: 120.20120.20

325 V peak

~230 V RMS EU line.

  • RMS Voltage: 230.00230.00

Visualization

RMS Values in Alternating Current

AC voltage and current vary with time. RMS (root mean square) is the DC value that would produce the same average power in a resistor.

For sinusoidal v(t) = V_peak sin(ωt): V_rms = V_peak/√2 ≈ 0.707 V_peak. Similarly I_rms = I_peak/√2.

Household mains (230 V EU, 120 V US) are quoted as RMS values. Peak voltage is √2 times higher (~325 V peak for 230 V RMS).

Average power: P_avg = V_rms I_rms cosφ (φ = phase angle). For pure resistor, cosφ = 1 and P = V_rms I_rms. Do NOT use V_peak I_peak for average power.

Other waveforms have different factors: square wave V_rms = V_peak; half-wave rectified sine has V_rms = V_peak/2.

Multimeters on AC range read RMS (for sine). Oscilloscopes often show peak-to-peak — convert before power calculations.

Key Concepts

  • V_rms = V_peak/√2 (sine wave)
  • I_rms = I_peak/√2
  • P_avg = V_rms I_rms cosφ
  • Mains ratings are RMS
  • Peak = √2 × RMS (sine)
  • Form factor depends on waveform

Real-World Applications

  • Mains voltage specification
  • AC power metering and billing
  • Component voltage rating (use peak or RMS correctly)
  • Audio signal levels (often RMS)
  • Class 12 alternating current

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Physics Equations

RMS Voltage:
Vrms=Vpeak2V_{rms} = \frac{V_{peak}}{\sqrt{2}}
Average Power:
Pavg=VrmsIrmsP_{avg} = V_{rms} I_{rms}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Waveform

Assume sinusoidal AC: v(t) = V_peak sin(ωt).

Explanation:

RMS formulas differ for square, triangular, or distorted waves — sinusoidal is standard for mains.

2

Step 2: RMS Definition

Equation:

Vrms=1T∫0Tv2(t) dtV_{rms} = \sqrt{\frac{1}{T}\int_0^T v^2(t)\,dt}

Explanation:

RMS is the square root of the mean of the squared function over one full cycle.

3

Step 3: RMS Voltage (Sine Wave)

Equation:

Vrms=Vpeak2V_{rms} = \frac{V_{peak}}{\sqrt{2}}

Calculation:

Vrms=1702=120.208153 VV_{rms} = \frac{170}{\sqrt{2}} = 120.208153 \text{ V}

Result:

Vrms=120.208153VV_rms = 120.208153 V

Explanation:

Peak is 1.4142× larger than RMS for sine waves. Mains "230 V" is RMS.

4

Step 4: RMS Current

Equation:

Irms=Ipeak2I_{rms} = \frac{I_{peak}}{\sqrt{2}}

Calculation:

Irms=12=0.707107 AI_{rms} = \frac{1}{\sqrt{2}} = 0.707107 \text{ A}

Result:

Irms=0.707107AI_rms = 0.707107 A

Explanation:

Same factor applies to current when waveform is sinusoidal and in phase with voltage (resistive load).

5

Step 5: Average Power in Resistor

Equation:

Pavg=VrmsIrmsP_{avg} = V_{rms} I_{rms}

Calculation:

Pavg=120.208153×0.707107=85.000000 WP_{avg} = 120.208153 \times 0.707107 = 85.000000 \text{ W}

Result:

Pavg=85.000000WP_avg = 85.000000 W

Explanation:

Do NOT use V_peak × I_peak — that overestimates average power by 2× for sine waves.

6

Step 6: Common Mistake — Average vs RMS

Contrast with rectified average voltage.

Calculation:

Half-wave rectified average≠Vrms;∣v∣avg=2Vpeakπ≈108.2254 V\text{Half-wave rectified average} \neq V_{rms}; \quad |v|_{avg} = \frac{2V_{peak}}{\pi} \approx 108.2254 \text{ V}

Explanation:

Meter on "AC" range reads RMS for sine. Oscilloscope may show peak or peak-to-peak — convert before power calc.

Frequently Asked Questions (FAQ)

Why √2?

RMS integrates sin² over a cycle; √(1/2) = 1/√2 factor between peak and RMS for sine.

Is 230 V dangerous peak or RMS?

RMS — peak is ~325 V, which matters for insulation breakdown.

DC has RMS equal to?

Constant value — V_rms = V_DC.

Peak-to-peak vs peak?

V_pp = 2 V_peak for symmetric sine. V_rms = V_peak/√2.

Three-phase RMS?

Line-to-line RMS relates to phase voltage; use √3 factors in balanced systems.

Practice MCQs

  1. 230 V RMS mains has peak voltage about:
  2. RMS stands for:
  3. For sine wave, V_rms / V_peak =
  4. Average power in resistor with AC uses:
  5. A square wave with peak 10 V has V_rms =
  6. Using peak instead of RMS for power calculation will:

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