Free online graphing tool
Sine Graph Calculator (y = a sin(bx + c))
The sine curve is the smooth wave that repeats every 2π radians (360°). It models everything that oscillates — alternating current, sound, tides, vibration and simple harmonic motion.
The graph below plots y = a sin(bx + c) with a slider for each parameter. Change a to stretch the wave vertically, b to squeeze more cycles into the same space, and c to slide the whole wave left or right.
Key points of y = a sin(b x + c) inside the visible window (-6.283 ≤ x ≤ 6.283). Pan or zoom to search a different range.
Roots (x-intercepts)
- x = -3.14159
- x = 0
- x = 3.14159
y-intercept
- y = 0
Turning points
- Max (-4.7124, 2)
- Min (-1.5708, -2)
- Max (1.5708, 2)
- Min (4.7124, -2)
Intersections
No crossing with another curve
Enter a value of x
What is a sine wave graph calculator?
A sine graph calculator plots y = a·sin(bx + c). The amplitude a is the height of each crest above the centre line, the period is 2π/b (or 360°/b in degrees), and the phase shift −c/b moves the wave horizontally. The curve repeats forever and always stays between −a and +a.
Key facts at a glance
| General form | y = a·sin(bx + c) + d |
|---|---|
| Amplitude | |a| — half the distance from crest to trough |
| Period (radians) | 2π / |b| |
| Period (degrees) | 360° / |b| |
| Phase shift | −c / b — negative moves the wave right |
| Vertical shift | d raises or lowers the centre line |
| Zeros of sin x | x = 0, ±π, ±2π, … (every multiple of π) |
| Range | −|a| + d ≤ y ≤ |a| + d |
How to plot sine wave graphs — step by step
- 1
Plot the basic wave
Type y = sin(x). The x-axis is already labelled in multiples of π on this page, so the period is easy to read.
- 2
Change the amplitude
Drag the a slider. The wave stretches vertically but the zeros stay exactly where they were.
- 3
Change the period
Drag b. Doubling b halves the period, so twice as many cycles fit into the same width.
- 4
Add a phase shift
Drag c to slide the wave sideways. y = sin(x + π/2) is identical to y = cos(x) — plot both to prove it.
- 5
Switch to degrees
Use the DEG toggle above the graph if your textbook works in degrees; sin(90) then equals 1 instead of 0.894.
Sine wave examples you can plot right now
Copy any equation into the calculator above, or open it in the full calculator with one click.
Sine and cosine together
y = cos(x)
Add this to y = sin(x): the two curves are the same shape, a quarter period apart.
Plot this →Damped oscillation
y = e^(-0.2x) sin(3x)
A sine wave inside a shrinking envelope — the physics of a settling spring.
Plot this →Understanding the sine wave graph
- Amplitude vs period
- Amplitude is a vertical measurement (how tall the wave is); period is a horizontal one (how long before it repeats). Changing one never changes the other.
- Radians vs degrees
- One full turn is 2π radians or 360°. Graphs are normally drawn in radians because the period then comes out as a clean multiple of π, which is why the x-axis here is labelled π/2, π, 3π/2 …
- Why sin and cos are the same curve
- cos(x) = sin(x + π/2). The cosine wave is simply the sine wave shifted a quarter of a period to the left, which is why they share amplitude, period and shape.
Sine wave graph — frequently asked questions
How do I graph a sine function online?
Type y = sin(x) into the calculator above. For a general wave use y = a sin(b x + c) — every letter that is not x automatically becomes a slider you can drag.
How do I find the amplitude and period from the equation?
For y = a·sin(bx + c) the amplitude is |a| and the period is 2π/|b| in radians, or 360°/|b| in degrees. The graph confirms it: measure crest height for amplitude and crest-to-crest distance for period.
What is the phase shift of a sine graph?
It is −c/b, the horizontal distance the wave has moved. A positive c inside the bracket shifts the wave to the LEFT, which catches most students out.
How do I switch the calculator to degrees?
Use the RAD/DEG toggle above the graph. In degree mode sin(90) = 1, and the x-axis is best read with the π labelling turned off in Graph settings.
Why does the x-axis show π/2 and π instead of numbers?
Because trigonometric graphs repeat over multiples of π, labelling the axis in π makes the period and the zeros obvious. You can turn it off under Graph settings.
How do I plot sin and cos on the same graph?
Type y = sin(x) in the first row and y = cos(x) in the second. Each gets its own colour, and the Key points tab lists exactly where the two curves cross.
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