Interpolation Calculator

How to use the Interpolation Calculator

1. 1Enter two points and the coordinate you know.
2. 2Pick the units or options from the menus if the linear interpolation tool offers them.
3. 3Read the linear interpolation in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the linear interpolation

People interpolate whenever they read a value between rows of a table: a tax table, a steam table, a calibration chart or a price list. Engineers, lab workers and students use it daily, and so do programmers who need a value between two samples.

The method is only as good as the straight-line assumption. For curves, use points that are close together, so that the line is a good approximation of the curve between them.

How the linear interpolation is worked out

y = y1 + (x − x1) × (y2 − y1) ÷ (x2 − x1). To find x from y, swap the roles: x = x1 + (y − y1) ÷ slope. With the points (2, 10) and (6, 30), the slope is 5. At x = 4 the line gives y = 10 + (4 − 2) × 5 = 20. At x = 8 the line gives 40, but that is outside the two points, so it is an extrapolation and less reliable.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Find y from x or x from y
• Slope and line equation shown
• Extrapolation warning

Mistakes to avoid with linear interpolation

Interpolating outside the two points is extrapolating, which is riskier because the real relationship may bend. Also, the two x values must be different, otherwise the line is vertical and no unique y exists.

On phone and computer

On a phone, type into the boxes one after another and read the linear interpolation underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the linear interpolation move. The interpolation calculator works the same on both. For line-based problems, Slope Calculator and Slope Intercept Form Calculator find the equation, Linear Regression Calculator fits many points, and Proportion Calculator solves a simple ratio.

Features

• Use close points for curves
• Extrapolation is risky
• The x values must differ
• Clear messages when the linear interpolation inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions