Sine Wave Calculator
Enter the amplitude, period, phase shift, and midline of a sinusoid and read off B, the frequency, the maximum and minimum, and the height of the wave at any x.
Wave properties
Reading a sinusoid
Every sine and cosine graph is a stretched, shifted copy of the parent wave. The four parameters in y = A·sin(B(x − C)) + D each control one transformation: A sets the height, B sets how tightly the cycles are packed, C slides the wave left or right, and D raises or lowers the whole thing. Once you can read those four numbers, you can sketch the curve without plotting points.
The calculator turns the period you enter into B and a frequency, then reports the midline, peak, and trough — the anchors you need to draw one clean cycle. Add an x value to evaluate the wave at a specific point.
Frequently Asked Questions
What do amplitude, period, phase shift, and midline mean?
In y = A·sin(B(x − C)) + D, the amplitude |A| is how far the wave rises above and falls below its centre line; the period is how long one full cycle takes; the phase shift C moves the wave horizontally; and the midline D moves it vertically. Together they stretch, squeeze, and slide the basic sine curve.
How are period, frequency, and B related?
They are three views of the same thing. B = 2π / period controls how fast the wave oscillates, and the frequency = 1 / period counts how many cycles fit in one unit of x. A shorter period means a larger B and a higher frequency.
How do I find the maximum and minimum?
A sine wave reaches D + |A| at its peak and D − |A| at its trough, because the sine factor swings between +1 and −1. The midline D sits exactly halfway between them. This tool reports all three so you can sketch the graph quickly.
Does this work for cosine waves too?
Yes. A cosine wave is just a sine wave shifted by a quarter period, so the same amplitude, period, frequency, midline, maximum, and minimum apply. If you're starting from a cosine form, convert the horizontal shift into a phase shift C and the rest carries over unchanged.
Educational tool only. Results are rounded for display; use full precision where an application requires it.