Sinusoidal regression calculator

For data that repeat, such as daylight hours, tides or temperatures over a year, fit a sine curve in one line. The Grapher finds a good starting point itself, so you do not have to guess the period.

The free IB Math Revision Grapher: A sine curve fitted to practice data: hours of daylight in each month of a year — A sine curve fitted to practice data: hours of daylight in each month of a year. Open it in the full Grapher.

How to do it

Enter your data. Paste or type the table. Use radians (the default): the period then comes out as 2π/b.
Type the sine model. Type y_1 ~ a sin(b x_1 + c) + d (or with cos). If you know the period, fix it: b = 2pi/12 on its own line holds b fixed in the fit.
Read the features. |a| is the amplitude, 2π/b the period and d the principal axis. What this model means words each one with your axis labels.
Check the residuals. Open the residual plot. Real periodic data are rarely a perfect sine curve: say what the pattern in the residuals tells you.

A sine curve fitted to monthly daylight hours in the Grapher, with the amplitude, period and principal axis explained — A sinusoidal fit with the amplitude, period and principal axis explained in context.

Good to know

A GDC's SinReg needs radian mode; so does this model's period 2π/b.
Many sets of parameters describe the same curve (a negative a with a shifted c, for example). The Grapher gives one of them; check it against the context.

Frequently asked questions

Do I need to guess the period first?

No. The Grapher searches for a good starting point itself before refining the fit. You can still fix the period yourself by defining b on its own line, for example b = 2pi/12.

How do I get the amplitude and period?

The amplitude is |a| and the period is 2π/b (in radians). The principal axis is y = d. “What this model means” lists them for your data.

Is it the same as SinReg on my GDC?

Both fit y = a sin(bx + c) + d by least squares. They can report different but equivalent parameters (for example a and c with different signs) for the same curve.

Learn more

More Grapher guides

The Grapher is our own free tool (graph.mathrevision.co.uk), built for IB, A Level and IGCSE students. It is not an exam calculator: practise on your own GDC for calculator papers.