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Linear Interpolation Calculator

Find any y value between two known points instantly

Known Points & Target

Point 1 (x₀, y₀)
Point 2 (x₁, y₁)

Result

Interpolated y22at x = 30
x₀ = 0x = 30x₁ = 100

30% of the way from x₀ to x₁

Point 1(0, 10)
Point 2(100, 50)
Target x30
Slope (Δy / Δx)0.4
Interpolated y22

Formula

y = y₀ + (x − x₀) × (y₁ − y₀) / (x₁ − x₀)

y = 10 + (30 − 0) × 0.4 = 22

How It Works

Linear interpolation
Estimating an unknown value that falls on a straight line between two known data points.
Formula
y = y₀ + (x − x₀) × (y₁ − y₀) / (x₁ − x₀) — the weighted average of the two y values.
Slope (Δy / Δx)
The rate of change between the two known points. Multiply by (x − x₀) to find the offset.
Extrapolation
When x falls outside the range [x₀, x₁] the same formula is used, but accuracy depends on whether the real data is truly linear beyond the known range.
About

A linear interpolation calculator lets you estimate an unknown y value that lies on a straight line between two known data points. Whether you're working with sensor readings, financial data, engineering measurements, or scientific tables, the lerp formula — y = y₀ + (x − x₀) × (y₁ − y₀) / (x₁ − x₀) — gives you an instant, accurate answer without spreadsheets or manual algebra.

FAQ
What is linear interpolation?+

Linear interpolation estimates a value between two known data points by assuming a straight-line relationship between them. Given points (x₀, y₀) and (x₁, y₁), the formula y = y₀ + (x − x₀) × (y₁ − y₀) / (x₁ − x₀) finds y for any x.

What is the difference between interpolation and extrapolation?+

Interpolation finds a value inside the range of the two known points (x₀ ≤ x ≤ x₁). Extrapolation uses the same formula but extends beyond that range. Extrapolation is less reliable because the data may not actually remain linear outside the known interval.

When would I use a linear interpolation calculator?+

Common uses include reading between rows in lookup tables, converting between unit scales, estimating temperature or pressure at an intermediate point, and filling in missing data values in engineering or scientific datasets.

What does the slope represent in linear interpolation?+

The slope (Δy / Δx) is the rate of change between the two known points. It tells you how much y changes for every one-unit increase in x. Multiplying the slope by the distance (x − x₀) gives you the y offset from y₀.

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