Period Calculator
Find the period of y = A·sin(Bx + C) + D and describe the full wave properties.
About Period Calculator
The period of y = A·sin(Bx + C) + D is 2π/|B| — the horizontal length of one complete cycle. Frequency is the reciprocal: |B|/(2π) cycles per x-unit.
Formula
Period
Period = 2π / |B|
- B
- Frequency coefficient
- T
- Period (one full cycle)
Worked example
With the default values below, Period Calculator returns Period of 2.094395. Change any input above and every figure here is recalculated in your browser.
Inputs used
- A (amplitude coefficient)
- 1
- B (frequency coefficient)
- 3
- C (phase constant)
- 0
- D (vertical shift)
- 0
Results
- Period
- 2.094395
- Frequency (cycles per unit)
- 0.477465
- Amplitude
- 1.000000
- Phase shift
- 0.000000
- Vertical shift (D)
- 0.0000
Step by step
- 1Period formula= 2.0943951
- 2Frequency= 0.47746483
- 3Amplitude= 1
- 4Phase shift= 0
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
What happens when B increases?
The period decreases (the wave compresses horizontally). B = 2 means 2 complete cycles in the interval [0, 2π].
How is period related to frequency?
Period = 1/frequency and frequency = 1/period. Period measures the length of one cycle; frequency measures cycles per unit.