Interpolação Linear
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
interp linear
About this calculator
The linear interpolation calculator finds the y value for a given x between two known points (x₁, y₁) and (x₂, y₂). The formula used is y = y₁ + (x − x₁) · (y₂ − y₁) / (x₂ − x₁), which assumes a linear variation between the points. It is useful for estimating missing data in tables or linear graphs.
The operation is simple: you enter the coordinates of the two points and the desired x value. The calculator applies the formula and returns the corresponding y. Linear interpolation is a numerical approximation technique, assuming the function between the points is a straight line.
Use this tool to fill gaps in experimental data, such as temperature versus time tables, or to calculate intermediate values in calibration curves. It is also common in finance to estimate interest rates for non-tabulated terms.
Caution: linear interpolation is only accurate if the relationship between the points is approximately linear. If there is significant curvature, the error can be large. Always check that x is between x₁ and x₂; extrapolation (outside the range) may give misleading results.
Frequently asked questions
Can I use linear interpolation for values outside the range of points?
Yes, but that is extrapolation and may be less accurate. The calculator allows it, but results should be used with caution as the linear trend may not hold.
What is the difference between linear interpolation and linear regression?
Linear interpolation uses exactly two points to estimate values between them, while linear regression fits a line to multiple points minimizing errors. Interpolation is deterministic; regression is statistical.
Does the calculator work with negative numbers?
Yes, it accepts negative and positive coordinates. The calculation follows the same formula regardless of sign.
How many decimal places should I use?
Use at least two decimal places for accuracy. The calculator rounds to two decimals, but you can input more; the result will be rounded.
Can I use it for interpolation in logarithm tables?
Yes, provided the variation between points is approximately linear. For nonlinear functions like logarithms, linear interpolation may have error, but it is acceptable for small intervals.