Quick answer

Enter A, B, C, D in f(x) = A sin(Bx - C) + D, select sine or cosine, and read phase shift C/B plus amplitude, period, and vertical shift.

Formula

  • Phase shift row: C / B
  • Period row: (2/B) × π rad
  • Amplitude row: A
  • Vertical shift row: D

Introduction

The tool is a static panel: your numbers never leave the browser. That makes it useful in classrooms and labs where you want quick confirmation without opening a computer algebra system.

Function input expects the expanded form. If your worksheet shows sin(B(x - h)), factor first so C inside Bx - C is correct.

Read how to calculate phase shift when you need pencil-and-paper steps before you type values into the panel.

Jump to the Phase Shift Calculator on our homepage while reading so you can mirror each bullet below with a live example.

Tool features and output meaning

Sine/cosine selection changes the trig function in the displayed formula line without altering how A, B, C, and D are interpreted.

Instant phase shift output updates as you type. There is no submit button because the math is lightweight enough to run on each keystroke.

Period appears as a coefficient times π radians, which matches how many textbooks write 2π/B.

Pair numeric readouts with worked phase shift examples so you recognize reasonable magnitudes before an exam.

Mapping inputs to formulas

  • f(x) = A sin(Bx - C) + D
  • Phase shift = C / B
  • Period = 2π / B

Use the same letter names as your textbook to avoid silent mismatches.

Degree and radian support: enter C as a decimal approximation when angles are not nice fractions of π.

Example calculations below the panel on the homepage give quick sanity checks you can reproduce in seconds.

Using the calculator efficiently

  1. Match the function. Choose sine or cosine to mirror the problem statement.
  2. Enter coefficients. Type A, B, C, and D from the expanded form.
  3. Read four outputs. Phase shift, amplitude, period, and vertical shift appear together.
  4. Watch for B = 0. Division by zero breaks period and phase readouts.
  5. Compare with a sketch. One cycle on paper should align with the reported shift and period.
  6. Save settings mentally. Repeat the same test case after you change only one parameter to see its effect.

Sample panel session

Enter A = 1, B = 2, C = 1.5708, D = 0 in sine mode. Phase shift ≈ 0.7854 (π/4) and period displays as 1 × π rad.

Switch to cosine with the same numbers to see how the formula line changes while the parameter meanings stay fixed.

Change only C to π and observe the phase shift row double while period stays the same because B did not change.