Amplitude, Period and Phase Shift Calculator

This amplitude, period and phase shift calculator reads the key features straight off a sinusoid written in the standard form y = A sin(Bx + C) + D, the equation used to describe waves, sound, tides, alternating current and any signal that repeats. You enter the four coefficients: A, the amplitude term; B, the coefficient of x inside the sine; C, the phase term; and D, the vertical shift. From these the calculator instantly returns the amplitude, the period, the phase shift and the vertical shift, updating as you type. The amplitude is how far the curve rises above and falls below its midline, worked out as the absolute value of A. The period is the length of one full cycle, found by dividing two pi by the absolute value of B. The phase shift shows how far the curve is moved left or right, calculated as minus C divided by B, with a positive result meaning a shift right. The vertical shift is simply D, the midline height the wave oscillates around. Note that the angle term Bx + C is always taken in radians, not degrees. This suits students checking homework and engineers wanting a quick, reliable read on a sinusoid's properties. A full worked example, the underlying formulas and the assumptions behind the results are set out below the calculator.

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