Amplitude And Period Calculator

Work out amplitude and period instantly with clear inputs, formula shown and shareable results.

About Amplitude And Period Calculator

For y = A·sin(Bx + C) + D the amplitude is |A|, the period is 2π/|B|, the graph is shifted horizontally by −C/B and vertically to the midline y = D. The range is D − |A| to D + |A|.

Formulas

Amplitude and period

amplitude = |A|, period = 2π / |B|

Phase shift

shift = −C / B (right if positive)

Worked example

With the default values below, Amplitude And Period Calculator returns Amplitude |A| of 3.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Amplitude coefficient A: 3
Frequency coefficient B: 2
Phase constant C: 1
Vertical shift D: 4

Results

Amplitude |A|: 3.0000
Period 2π/|B|: 3.14159265
Phase shift −C/B: -0.50000000
Midline y = D: 4.0000

Step by step

1Values used
2Amplitude and period
3Phase shift
4Amplitude |A|= 3.0000
5Period 2π/|B|= 3.14159265
6Phase shift −C/B= -0.50000000
7Midline y = D= 4.0000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For y = 3 sin(2x + 1) + 4?

Amplitude 3, period π ≈ 3.141593, phase shift −0.5 and midline y = 4.

Does the period change for cosine?

No. Sine and cosine share the same amplitude and period rules; only the starting phase differs.