Fourier Series Calculator (Standard Waveforms)
Fourier coefficients, partial sums and RMS value for square, triangle, sawtooth and rectified sine waves.
How to use the Fourier Series Calculator
- Enter or select: Waveform, Amplitude A, Frequency f, Number of harmonics, Time t.
- The results (DC term a₀/2, Coefficients (first harmonics), Partial sum at t, Exact value at t, Difference, RMS of waveform, Energy of harmonics shown) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- x(t) = a₀/2 + Σ [aₙcos(nωt) + bₙsin(nωt)]
- Square: bₙ = 4A/(nπ), n odd
- Triangle: bₙ = 8A(−1)^((n−1)/2)/(π²n²), n odd
- Sawtooth: bₙ = (2A/nπ)(−1)^(n+1)
About this tool
Near jump discontinuities the partial sums overshoot by about 9 % (Gibbs phenomenon) however many harmonics are used.