Sine Wave Calculator & Plotter
Plot a sine wave y = A·sin(2πft + φ). Enter amplitude, frequency and phase to see the waveform, period, angular frequency and RMS value.
How to use this tool
- Enter amplitude (a), frequency (hz), phase shift (°) and cycles to plot in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your period (s) and the full breakdown beneath it.
A sine wave is described by y(t) = A · sin(2πft + φ), where A is amplitude, f is frequency in Hz, and φ is the phase in radians. The RMS value of a pure sine wave is A / √2.
Formula
y(t) = A × sin(2πft + φ)
Period T = 1 / f | Angular frequency ω = 2πf | RMS = A / √2
Where A = amplitude, f = frequency (Hz), φ = phase shift (radians), t = time (s).
How it works
The calculator evaluates y(t) = A sin(2πft + φ) at evenly spaced time steps across the requested number of cycles, producing a waveform chart. The phase angle entered in degrees is converted to radians internally (φ = degrees × π / 180). The RMS (root mean square) value A / √2 applies to a pure sinusoid and represents the equivalent DC power level; it is exact only for a full, unclipped sine wave with zero DC offset.
Worked example
- Amplitude A = 1, frequency f = 1 Hz, phase shift = 0°, cycles to plot = 2.
- Period T = 1 / 1 = 1.0 s.
- Angular frequency ω = 2π × 1 = 6.2832 rad/s.
- Peak value = A = 1.
- RMS value = 1 / √2 = 0.7071.
Period: 1.0 s; Angular frequency: 6.2832 rad/s; Peak value: 1; RMS value: 0.7071.
Common mistakes to avoid
- Entering phase shift in degrees instead of radians — the formula uses radians, so a 90-degree shift should be entered as approximately 1.5708, not 90.
- Confusing frequency (Hz) with period (seconds) — a 2 Hz wave has period T=0.5 s; entering 2 when you mean a 2-second period produces a wave 4x faster than intended.
- Treating the RMS value as the peak amplitude — RMS = A/sqrt(2), so a 10-unit amplitude wave has RMS approximately 7.07, not 10.
Key terms
- Amplitude (A)
- The peak displacement of the wave from zero. The waveform oscillates between −A and +A.
- Frequency (f)
- The number of complete cycles per second, measured in hertz (Hz).
- Period (T)
- The time for one complete cycle, T = 1 / f.
- Angular frequency (ω)
- The rate of change of the wave's phase in radians per second, ω = 2πf.
- RMS value
- Root mean square: for a pure sine wave, RMS = A / √2 ≈ 0.7071 × A. It equals the DC voltage that delivers the same average power.
Frequently asked questions
- What is the RMS value used for?
- Root-mean-square (RMS) voltage or current tells you the effective power of an AC signal. Mains electricity (e.g. 120 V / 230 V) is quoted in RMS.
- What is angular frequency?
- Angular frequency ω = 2πf, measured in radians per second. It's often more convenient in equations than ordinary frequency f.