Linear Interpolation Calculator

Finds a value between two known points by linear interpolation, looks up in-between values in a table, and does bilinear interpolation in a 2-D table. Use it when a steam table, property table or conversion table does not list the exact value you need.

How to use

1. On "Between two points", enter x₁, y₁, x₂ and y₂, choose "y from x" or "x from y" under "Find", and enter the known value.
2. The result appears with the "Working" and a label that says whether it is interpolated or extrapolated.
3. To look up many values, paste a table on "Table lookup", enter the "x values to look up", and press "Copy results".
4. When a value depends on two variables, open "Bilinear (2-D)" and enter the four corner values or a 2-D table.

How it works

• Linear interpolation: y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁). It assumes a straight line between the two points.
• Bilinear interpolation interpolates twice along x, then once along y between those two results.
• "Table lookup" sorts rows by x and averages repeated x values. Values outside the table are calculated only with extrapolation switched on.
• Pasted data and your inputs are saved only in this browser on this device.

Questions and answers

How do you calculate linear interpolation?

Multiply the slope between the two points by the distance from x₁ and add it to y₁. For (100, 2.5) and (110, 3.1) at x = 104, y = 2.5 + 4 × 0.06 = 2.74.

What is the difference between interpolation and extrapolation?

Interpolation finds a value between the two points; extrapolation finds one outside them. Extrapolation extends the line beyond the data, so use it with care.

When do I need bilinear interpolation?

When a table is read with two values, such as temperature and pressure, and both fall between the listed rows and columns.

Can I do linear interpolation in Excel?

FORECAST.LINEAR with exactly two points gives the same result. Given a whole table, it fits a regression line instead, which is not interpolation between neighbouring rows.