Linear Interpolation Calculator
Estimate a value between two known data points using linear interpolation (LERP).
This free online linear interpolation calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
The x value at which to estimate y
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Linear Interpolation Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Linear Interpolation Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Linear Interpolation Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Linear Interpolation Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
- •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
- •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
- •Use it to explore the behavior of mathematical functions across a range of inputs.
About This Calculator
The Linear Interpolation Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Estimate a value between two known data points using linear interpolation (LERP). The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.
About Linear Interpolation Calculator
Linear interpolation (often abbreviated LERP) estimates a value between two known data points by assuming a straight-line relationship. Given two points (x0, y0) and (x1, y1), and a target x value between x0 and x1, the interpolated y value lies on the straight line connecting the two points. This technique is ubiquitous in numerical analysis, computer graphics (color blending, animation), engineering (reading between table entries), and data science (filling in missing data). It is the simplest form of interpolation and provides exact results when the underlying relationship is truly linear. For nonlinear data, it gives an approximation whose accuracy depends on how close together the data points are. The interpolation parameter t ranges from 0 (at the first point) to 1 (at the second point), providing a normalized measure of position between the two endpoints.
The Math Behind It
Formula Reference
Linear Interpolation (LERP)
y = y₀ + ((x - x₀) / (x₁ - x₀)) × (y₁ - y₀)
Variables: (x₀, y₀), (x₁, y₁) = known points; x = target value between x₀ and x₁
Parametric Form
y = (1 - t) × y₀ + t × y₁, where t = (x - x₀) / (x₁ - x₀)
Variables: t = interpolation parameter (0 at first point, 1 at second point)
Worked Examples
Example 1: Interpolating between two data points
Known: (1, 10) and (5, 30). Estimate y at x = 3.
At x = 3, y = 20
Example 2: Interpolation with non-midpoint target
Known: (0, 100) and (10, 200). Estimate y at x = 7.
At x = 7, y = 170
Common Mistakes & Tips
- !Using extrapolation (t outside 0 to 1) without recognizing reduced accuracy.
- !Swapping x0 and x1, which changes the sign of t.
- !Applying linear interpolation to highly nonlinear data without considering the error.
- !Confusing the x and y roles in the formula.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
What is the difference between interpolation and extrapolation?
Interpolation estimates within the range of known data (t between 0 and 1). Extrapolation estimates outside the range (t < 0 or t > 1) and is less reliable.
How accurate is linear interpolation?
It is exact for linear data. For smooth nonlinear data, the error decreases quadratically as the data points get closer together.
What is bilinear interpolation?
Bilinear interpolation extends LERP to 2D grids by performing linear interpolation in one direction, then in the other direction. It is commonly used in image processing.