Free · Mathematical relationships

Linear Interpolation through Two Points

Two points with distinct x coordinates define a line. Interpolation uses its value between the points; outside that interval the same calculation is extrapolation.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With x1 = 1, y1 = 3, x2 = 5, y2 = 11, x3 = 3, slope = 2, intercept = 1, y3 = 7.

m=(y₂−y₁)/(x₂−x₁); y=mx+b

Worked example

Enter these known values and leave the other values blank.

x₁: 1
y₁: 3
x₂: 5
y₂: 11
x₃: 3

y₃: 7
m: 2
b: 1

Assumptions and limitations

All x coordinates must be distinct in this workflow. A horizontal line evaluates forward at a supplied x but does not determine an unknown x.
Two points with distinct x coordinates define a line. Interpolation uses its value between the points; outside that interval the same calculation is extrapolation.
Enter enough independent values and clear the quantity being solved. Locks preserve known values; contradictory inputs can make the system inconsistent. Unit controls convert physical quantities rather than merely changing their labels.
Displayed precision is numerical rounding, not an estimate of measurement uncertainty.

Common questions

How do I solve for a missing quantity?

Clear the missing value, enter the independent known values and retain compatible units. A nonunique inverse may require another known value.

What relationship is used?