Interpolation Calculator

Estimate a value between known data points using linear interpolation.

Inputs

x₀ (known)

y₀ = f(x₀)

x₁ (known)

y₁ = f(x₁)

x (target)

Interpolated y

5.00000000

Slope

3.00000000

Step by step

Values used
x₀ (known) = 1; y₀ = f(x₀) = 2; x₁ (known) = 3; y₁ = f(x₁) = 8; x (target) = 2
Linear interpolation
y = y₀ + (y₁ - y₀) · (x - x₀) / (x₁ - x₀)
Interpolated y
= 5.00000000
Slope
= 3.00000000

How it works

Linear interpolation estimates f(x) between two known points (x₀,y₀) and (x₁,y₁) by drawing a straight line between them: y = y₀ + (y₁-y₀)·(x-x₀)/(x₁-x₀). This is exact for linear functions and a first-order approximation for nonlinear ones.

Formula

Linear interpolation

y = y₀ + (y₁ - y₀) · (x - x₀) / (x₁ - x₀)

(x₀,y₀): First known point
(x₁,y₁): Second known point
x: Target x value

Frequently Asked Questions

When is linear interpolation accurate?

When the function is approximately linear between the two points, or when the points are close together. For curved data, use polynomial or spline interpolation.

What about extrapolation?

The same formula works for x outside [x₀,x₁], but accuracy degrades quickly. Extrapolation should be used cautiously.

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