What is amplitude?
The maximum distance from the midline; for A sin or A cos it is |A|.
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.
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
- Choose sine or cosine form.
- Enter A, B, and optional phase C.
- Select Calculate to view amplitude and period.
- 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 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.