Linear Interpolation Calculator is designed for the exact search intent behind “linear interpolation calculator”. Estimate a y-value between two known coordinate points by assuming the change between them is linear. Enter the two points and the target x-value to calculate the corresponding value on the straight line. Estimate y at a target x between two known (x,y) points using a straight-line assumption. Linear interpolation formula For known points (x₁, y₁) and (x₂, y₂), the value at x is: y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁) How linear interpolation works The fraction (x − x₁)/(x₂ − x₁) tells you how far x lies through the known x-interval. Applying the same fraction to the change from y₁ to y₂ gives the estimated y-value. Interpolation vs. extrapolation Interpolation uses an x-value inside the known interval. A value outside the interval is extrapolation. The same line formula can produce a number, but extrapolation usually carries more uncertainty because the observed relationship may not remain linear outside the known range. Worked example: For x = 15: y = 20 + (15−10) × (40−20)/(20−10) = 20 + 10 = 30. Common practical uses include Estimate values inside engineering or scientific tables; Interpolate calibration data between known measurements; Estimate a missing point in approximately linear data; Check spreadsheet or programming interpolation calculations. Important limitations: Linear interpolation assumes the relationship between the known points can reasonably be represented by a straight line. x₁ and x₂ cannot be equal because the formula would divide by zero. Using a target x outside the known interval is extrapolation, not interpolation, and can be substantially less reliable. Key questions this page should answer include: What is the linear interpolation formula? y = y₁ + (x − x₁)(y₂ − y₁)/(x₂ − x₁). What does linear interpolation calculate? It estimates a value between two known points by assuming a constant rate of change along the straight line connecting them. Can x be outside x₁ and x₂? The line formula can still return a value, but that is extrapolation rather than interpolation and is generally less reliable. What happens if x₁ equals x₂? The standard formula is undefined because x₂ − x₁ is zero. When should I not use linear interpolation? Avoid treating it as accurate when the underlying relationship is strongly curved, discontinuous or otherwise not approximately linear between the known points.
How to use this tool
Linear interpolation formula
For known points (x₁, y₁) and (x₂, y₂), the value at x is:
y = y₁ + (x − x₁) × (y₂ − y₁) ÷ (x₂ − x₁)
How linear interpolation works
The fraction (x − x₁)/(x₂ − x₁) tells you how far x lies through the known x-interval. Applying the same fraction to the change from y₁ to y₂ gives the estimated y-value.
Interpolation vs. extrapolation
Interpolation uses an x-value inside the known interval. A value outside the interval is extrapolation. The same line formula can produce a number, but extrapolation usually carries more uncertainty because the observed relationship may not remain linear outside the known range.
Examples
Interpolate between (10, 20) and (20, 40)
For x = 15: y = 20 + (15−10) × (40−20)/(20−10) = 20 + 10 = 30.
Common use cases
- Estimate values inside engineering or scientific tables
- Interpolate calibration data between known measurements
- Estimate a missing point in approximately linear data
- Check spreadsheet or programming interpolation calculations
Frequently asked questions
What is the linear interpolation formula?
y = y₁ + (x − x₁)(y₂ − y₁)/(x₂ − x₁).
What does linear interpolation calculate?
It estimates a value between two known points by assuming a constant rate of change along the straight line connecting them.
Can x be outside x₁ and x₂?
The line formula can still return a value, but that is extrapolation rather than interpolation and is generally less reliable.
What happens if x₁ equals x₂?
The standard formula is undefined because x₂ − x₁ is zero.
When should I not use linear interpolation?
Avoid treating it as accurate when the underlying relationship is strongly curved, discontinuous or otherwise not approximately linear between the known points.