# Linear Interpolation Calculator

URL: https://speedycalculator.com/calculators/math/linear-interpolation/
Last updated: 2026-10-25

> The linear interpolation calculator estimates a value between two known points by assuming a straight line between them. It is used with tables, sensors and engineering data.

## Inputs

- x₁
- y₁
- x₂
- y₂
- x (to estimate)

## Results

- Interpolated y

## Formula

```
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)
```

## Explanation

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

FieldWhat to enterx₁A numbery₁A numberx₂A numbery₂A numberx (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 y74110.551.5146217.572.5218328104

## Worked example

Inputs — x₁: 10; y₁: 50; x₂: 20; y₂: 80; x (to estimate): 14.

Results — **Interpolated y = 62**.

## FAQ

**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).