⚙️

Amplitude Calculator

Free amplitude calculator — find amplitude, period, frequency, and phase shift of y = A·sin(Bx + C) + D, with a live animated wave.

y = A · sin(B·x + C) + D — enter values to animate the wave

Amplitude (A)

Known value — choose which

Phase term C (in sin(Bx + C), optional)

Vertical shift D (optional)

Enter amplitude and any one of period / frequency / angular frequency — the rest are derived from y = A·sin(Bx + C) + D.

Enter the amplitude and a period, frequency, or angular frequency — the moving wave above and all derived values update instantly.

Loading…

Everyday Uses

Sound & music

Amplitude is loudness and frequency is pitch — model a note or tone and see how its wave changes.

Reading a sine wave equation

Read A, period, frequency, and phase shift straight off y = A·sin(Bx + C) + D, with the wave drawn for you.

AC electricity

Mains power is a sine wave — amplitude is peak voltage, frequency is 50 or 60 Hz, phase matters for three-phase systems.

Waves & vibration

Springs, pendulums, light, and ocean waves all follow this equation — visualize any of them instantly.

How far a tall building may sway

Skyscrapers and footbridges are designed to a permitted sway amplitude. Exceeding it is not a collapse risk so much as a comfort one — occupants feel motion long before anything is structurally at stake.

Watching a swing die away

Compare amplitude cycle by cycle in a pendulum or a car suspension and you can see how much energy each bounce is absorbing — the practical measure of damping.

Frequently Asked Questions

What is amplitude?

Amplitude is the maximum distance a wave moves from its midline (resting position). In y = A·sin(Bx + C) + D it equals |A|. A taller wave has a larger amplitude — for sound it means louder, for light brighter, for a spring a wider swing. It is always a positive value, since it measures a distance.

How are period and frequency related?

They are reciprocals: frequency = 1 / period, and period = 1 / frequency. The period is how long one full cycle takes; the frequency is how many cycles happen per unit (per second = hertz). In y = A·sin(Bx + C), the period is 2π/B and the frequency is B/2π. A wave that repeats every 0.5 seconds has a frequency of 2 Hz.

What is phase shift?

Phase shift is how far the wave is moved horizontally (left or right) compared with a plain sine wave. For y = A·sin(Bx + C), the phase shift is −C/B. A positive shift moves the wave left, negative moves it right. It is what makes two waves "in phase" (aligned) or "out of phase" (offset), which matters hugely in audio, optics, and AC electricity.

What do B, C and D mean in the equation?

In y = A·sin(Bx + C) + D: A is amplitude (height); B is the angular frequency, which sets the period (2π/B) and how tightly packed the cycles are; C shifts the wave horizontally (phase shift −C/B); and D shifts the whole wave vertically (the midline moves to y = D). This calculator lets you enter amplitude plus any one of period, frequency, or B and derives the rest.