Amplitude Calculator
Find the amplitude of y = A·sin(Bx + C) + D and describe the full wave properties.
About Amplitude Calculator
The amplitude of y = A·sin(Bx + C) + D is |A| — the distance from the midline (y = D) to the peak. The wave oscillates between D − |A| and D + |A|.
Formula
Amplitude
Amplitude = |A|
- A
- Coefficient of the trig function
- D
- Vertical shift (midline)
Worked example
With the default values below, Amplitude Calculator returns Amplitude of 3.000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- A (amplitude coefficient)
- 3
- B (frequency coefficient)
- 1
- C (phase constant)
- 0
- D (vertical shift)
- 0
Results
- Amplitude
- 3.000000
- Maximum y-value
- 3.000000
- Minimum y-value
- -3.000000
- Period
- 6.283185
- Phase shift
- 0.000000
- Vertical shift (D)
- 0.0000
Step by step
- 1Amplitude formula= 3
- 2Maximum value= 3
- 3Minimum value= -3
- 4Period= 6.28318531
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 6 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
Can amplitude be negative?
No — amplitude is always |A|, a non-negative number. A negative A flips the wave vertically but doesn't change the amplitude.
How does amplitude relate to the wave height?
The total peak-to-trough height is 2·|A|. Amplitude is half of that — the distance from the midline to a peak.