What is linear interpolation?

Linear interpolation is a mathematical technique used to estimate an unknown intermediate value between two known data points (x₁, y₁) and (x₂, y₂), assuming a straight-line relationship between them.

What is the linear interpolation formula?

The formula is: y = y₁ + [(x − x₁) / (x₂ − x₁)] × (y₂ − y₁) . Alternatively expressed in slope-intercept form: y = y₁ + m × (x − x₁), where m = (y₂ − y₁) / (x₂ − x₁).

What is bilinear interpolation?

Bilinear interpolation extends linear interpolation into two dimensions. It interpolates functions of two variables (x, y) on a rectilinear 2D grid using values at four surrounding corner points.

Interpolation Calculator

Linear & 2D Bilinear Interpolation with Steps

Point 1 (x₁, y₁)

x₁

y₁

Point 2 (x₂, y₂)

x₂

y₂

Target Interpolation Point (x)

Enter target x to find y:

Interpolate value $f(x,y)$ on a 2D rectangular grid given 4 corner points.

x₁

x₂

y₁

y₂

Corner Values f(x, y):

Target x

Target y

Interpolated Result

Interpolated Value (y)

12.0000

At point x = 5

Step-by-Step Solution:

y = y₁ + [(x − x₁) / (x₂ − x₁)] × (y₂ − y₁)
y = 6 + [(5 − 2) / (8 − 2)] × (18 − 6)
y = 6 + [3 / 6] × 12
y = 6 + 0.5 × 12
y = 6 + 6 = 12.0000
                