Math Calculator

Amplitude and Period Calculator

Enter A, B, and C for y = A sin(Bx+C) or A cos(Bx+C) to get amplitude and period.

Enter wave coefficients

Use the form A sin(Bx+C) or A cos(Bx+C). Phase C does not change amplitude or period.

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About this calculator

How to use Amplitude and Period Calculator, plus the formulas and logic behind the results.

Tool description

For y = A sin(Bx+C) or A cos(Bx+C), the amplitude is |A| and one full cycle has period 2π/|B| (radians).

How to use

  1. Choose sine or cosine form.
  2. Enter A, B, and optional phase C.
  3. Select Calculate to view amplitude and period.
  4. Confirm B ≠ 0 so the period is defined.

Formulas & reference

  • Amplitude = |A|
  • Period = 2π / |B|
  • Phase shift (radians) = −C/B when B ≠ 0

Examples

  • 3 sin(2x) → amplitude 3, period π
  • −2 cos(x) → amplitude 2, period 2π
  • B = 0 is not a periodic sinusoidal form here
  • C shifts the graph horizontally

Calculation logic

Takes absolute value of A for amplitude and divides 2π by |B| for period. Phase is reported for reference.

Angles are in radians. Convert degrees to radians before entering C if your source uses degrees.

Amplitude and Period Calculator FAQ

Common questions about this calculator and how to use the results.

What is amplitude?

The maximum distance from the midline; for A sin or A cos it is |A|.

What is period?

The horizontal length of one full cycle: 2π/|B| for these forms.

Does C affect amplitude?

No. Phase shift moves the graph but does not change height or period.

What if A is negative?

The wave is reflected; amplitude is still |A|.

Are units radians or degrees?

This calculator treats Bx+C in radians.

Why must B be nonzero?

If B = 0 the expression is constant and has no sinusoidal period.