Signals & Systems
Signal Metrics Calculator
RMS, mean, average power, energy, peak, peak-to-peak, and crest factor of a signal — generated from a standard waveform or entered as samples.
About this calculator
The everyday amplitude and energy figures of a signal, computed from its samples with each definition shown. Enter your own samples or generate a standard waveform, and the tool reports the mean (DC level), the RMS value, the average (mean-square) power, the total energy, the peak and peak-to-peak amplitudes, and the crest factor.
These quantities are the ones that show up in every practical setting: RMS is what an AC meter reads and what sets heating in a resistor; crest factor (peak/RMS) tells you how much headroom a converter or amplifier needs above the RMS level; average power and energy distinguish power signals (finite average power, infinite energy — like a steady tone) from energy signals (finite total energy — like a pulse).
For the standard waveforms the results match the classic closed forms — a sine of amplitude A has RMS = A/√2 and crest factor √2; a square wave has RMS = A and crest factor 1; a symmetric triangle has RMS = A/√3. Generating a whole number of periods makes the sampled statistics land exactly on those values, which is a good way to confirm both the tool and your own hand calculation.
Design notes & common mistakes
- RMS = √(mean of squares). For a full-cycle sine it is A/√2 ≈ 0.707A; for a square wave it is A; for a symmetric triangle it is A/√3.
- Crest factor (peak/RMS) sets required headroom: 1 for a square wave, √2 for a sine, larger for peaky signals — it is why amplifiers are rated well above their RMS output.
- Average power P = x²_rms; total energy is Σx² (multiply by the sample period Ts for the continuous-time energy).
- A DC offset raises RMS: total power splits into DC power (x̄²) plus AC power (variance). Subtract the mean to get the AC-only figure.
Assumptions
- Metrics are computed from the samples exactly as given or generated (discrete sums, no interpolation).
- Generated waveforms cover a whole number of periods so the sampled statistics match the closed-form values.
- Energy is the per-sample discrete energy Σx²; multiply by the sample period for the continuous-time value.
- Real-valued samples; a record of up to 4096 samples is supported.
When to use this calculator
Appropriate for
- Computing RMS, power, energy, peak, and crest factor of a sampled signal
- Checking hand calculations against the closed-form sine/square/triangle values
- Teaching the difference between energy and power signals and the meaning of crest factor
Not suitable for
- Spectral or harmonic-distortion analysis (use the DFT or Fourier-series tools)
- Calibrated physical-unit measurements without a defined sample rate and load
- Non-stationary signals where a single RMS over the record is misleading
What this calculator does not cover
- Amplitude/energy statistics only — no frequency-domain measures (see the DFT analyzer for spectral content).
- Real-valued signals; complex or vector signals are out of scope.
- Discrete per-sample energy; it is not scaled to physical joules without a stated sample period and load.
- No windowing or trend removal — a partial-period record biases the RMS and mean.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is the RMS value of a sine wave?
For a sine of peak amplitude A, the RMS value is A/√2 ≈ 0.707A. RMS is the heating-equivalent level — a resistor dissipates the same average power from the sine as from a steady DC equal to the RMS value. A square wave's RMS equals its amplitude A; a symmetric triangle's is A/√3.
What does crest factor tell me?
Crest factor is the ratio of peak to RMS amplitude. It measures how 'peaky' a signal is and therefore how much headroom above the RMS level a converter or amplifier must reserve. A sine has crest factor √2 ≈ 1.41; a square wave, 1; noisy or impulsive signals, much higher.
What is the difference between energy and power signals?
An energy signal has finite total energy (Σx²) and zero average power — a pulse, for example. A power signal has finite average power but infinite total energy — a steady tone. RMS and average power characterize power signals; total energy characterizes energy signals.
References
- Lathi, B. P., Linear Systems and Signals, 2nd ed., Ch. 1 (signal energy and power, RMS)
- Proakis, J. G. & Manolakis, D. G., Digital Signal Processing, 4th ed., Ch. 1 (signal metrics)
- IEEE Std 181 (definitions of pulse peak, amplitude, and related measures)
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