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
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
Interpolation
Finding values between known data points
More reliable and accurate
Extrapolation
Finding values outside known data range
Less reliable, use with caution
Key Formulas
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