When a table only lists certain values, interpolation estimates what lies between them.
How to use the Linear Interpolation Calculator
- x₁
- y₁
- x₂
- y₂
- x (to estimate)
- Want to work backwards? Type a value into Interpolated y and x (to estimate) is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Find how far x lies between x₁ and x₂ as a fraction, then move that same fraction from y₁ toward y₂.
Inputs explained
| Field | What to enter |
|---|---|
| x₁ | A number |
| y₁ | A number |
| x₂ | A number |
| y₂ | A number |
| x (to estimate) | A number |
Example values
How the main result changes when x changes and everything else stays at the example values above:
| x (to estimate) | Interpolated y |
|---|---|
| 7 | 41 |
| 10.5 | 51.5 |
| 14 | 62 |
| 17.5 | 72.5 |
| 21 | 83 |
| 28 | 104 |
Formula
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)Worked example
Inputs — x₁: 10; y₁: 50; x₂: 20; y₂: 80; x (to estimate): 14.
Results — Interpolated y = 62.
Frequently asked questions
Can x be outside the range?
Yes, but that is extrapolation and is less reliable.
Is linear interpolation exact?
Only if the data really follow a straight line between the points.
What formula does the Linear Interpolation Calculator use?
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁).
Can I work backwards from the result?
Yes. Type the result you want into Interpolated y and the calculator finds the matching x (to estimate).