Linear Interpolation Calculator

Find values between known data points using linear interpolation and extrapolation

Linear Interpolation Calculator

Known Data Points

Find y for given x

Invalid Input

Please ensure that the two points are different. Both x and y coordinates cannot be identical.

Example: Cookie Baking Problem

Problem Statement

You used 200g of flour to bake 15 cookies, and 300g of flour to bake 20 cookies. How many cookies can you bake with 250g of flour?

Solution

Given points: (200, 15) and (300, 20)

Find y when x = 250

Formula: y = (x - x₁) × (y₂ - y₁) / (x₂ - x₁) + y₁

Calculation: y = (250 - 200) × (20 - 15) / (300 - 200) + 15

Result: y = 50 × 5 / 100 + 15 = 2.5 + 15 = 17.5 cookies

Interpolation vs Extrapolation

I

Interpolation

Finding values between known data points

More reliable and accurate

E

Extrapolation

Finding values outside known data range

Less reliable, use with caution

Key Formulas

Linear Interpolation:
y = (x - x₁) × (y₂ - y₁) / (x₂ - x₁) + y₁
Slope:
m = (y₂ - y₁) / (x₂ - x₁)
Y-Intercept:
b = y₁ - m × x₁
Distance:
d = √[(x₂-x₁)² + (y₂-y₁)²]

Tips

Interpolation is more accurate than extrapolation

Linear interpolation assumes constant rate of change

Check if linear relationship is reasonable for your data

Be cautious with extrapolation beyond known range

Understanding Linear Interpolation

What is Linear Interpolation?

Linear interpolation is a method for estimating unknown values that fall between two known values. It assumes that the relationship between the variables is linear (straight line) within the range of the known data points.

When to Use Linear Interpolation

  • When you have two known data points
  • When the relationship appears to be linear
  • For quick estimates between known values
  • In engineering and scientific calculations

Applications

Engineering

Material properties, temperature effects, pressure calculations

Economics

Market trends, price predictions, demand forecasting

Science

Experimental data analysis, calibration curves

Computer Graphics

Animation, image scaling, color gradients

Limitations

  • Assumes linear relationship (may not be accurate for curved data)
  • Extrapolation can be unreliable
  • Only works with two data points