Interpolation Calculator

Interpolation Calculator

Enter your data points, pick a method, and get the interpolated value with a graph and step-by-step working. Free, no sign-up.

Calculator

Coordinate Points

2/10 points
XY
Try an example
Interpolation method

Leave blank to plot the curve without a single lookup value.

Quick help guide

Everything you need to know to get started.

Troubleshooting
JavaScript issues
The calculator requires JavaScript. Please ensure it is enabled in your browser.
Input requirements
All x-coordinates must be unique. Duplicate x values are not allowed.
Minimum points
Linear interpolation needs at least 2 points. Cubic spline requires 3 or more.

How to use
  1. Enter data points. Add at least two points by entering x and y coordinates.
  2. Choose a method. Select linear, polynomial, or cubic spline interpolation.
  3. Set an interpolation point. Optional. Enter the x value where you want the interpolated y value.
  4. Calculate. See the result with a graph and step-by-step working.

Input format

The calculator accepts:

  • Integers: 1, 2, 42, -5
  • Decimals: 1.5, 3.14, -0.5 (use period, not comma)
  • Scientific notation: 1e3, 2.5e-2

CSV import format

Use two columns: the first for x-values, the second for y-values.

Where interpolation is used

The same three methods turn up across a lot of very different fields.

Computer graphics
Create smooth animations and curves for visual effects.
Data analysis
Fill gaps in datasets and estimate intermediate values.
Digital design
Generate smooth curves for vector graphics and CAD.
Scientific research
Analyze experimental data and build mathematical models.
Engineering
Design optimization and structural analysis.
Machine learning
Feature engineering and data preprocessing.

Why use this calculator

Built for real work, not just a quick answer.

High precision
Results carried at full floating-point precision, shown to 4 decimal places.
Interactive visualization
A live graph of your points and the fitted curve, with hover tooltips.
Easy data sharing
Import points from CSV and export your results back out in one click.
Educational
Every calculation comes with the working, step by step.

Frequently asked questions

Common questions about interpolation, data analysis, and using the calculator.

View all FAQs Tutorial guide Calculation accuracy

What is interpolation and why is it useful?
Interpolation is a mathematical technique for estimating values between known data points. It's useful for filling gaps in datasets, creating smooth curves from discrete measurements, and predicting intermediate values. Our calculator supports multiple methods to handle different types of data. Learn more in our comprehensive tutorial section.

Which interpolation method should I choose?
For simple, linear relationships between points, choose linear interpolation. For complex curves with few points, polynomial interpolation works well. For larger datasets or when stability is important, cubic spline interpolation provides the best balance. See our accuracy disclaimer for more information on method selection.

How do I interpret the interpolation results and graphs?
Our results section displays the interpolated value at your requested point, the derived mathematical function, and a visual graph plotting both your original data points and the interpolation curve. For polynomial and cubic spline methods, we also provide the coefficient values and equations for each segment. The graph helps you visualize how well the chosen method fits your data.

Is it possible to import data from Excel or other spreadsheet programs?
Yes, you can import data directly from Excel, Google Sheets, or any spreadsheet program by saving your data as a CSV file. Your file should have two columns (for x and y values), with or without headers. Use our 'Import CSV' feature to quickly load your data points into the calculator, saving time and reducing input errors.

What are the common applications of interpolation in different fields?
Interpolation is widely used across disciplines: in engineering for stress analysis and signal processing; in meteorology for weather prediction between weather stations; in finance for estimating missing market data; in computer graphics for creating smooth animations; in geography for contour mapping; and in medicine for interpreting lab results and medical imaging. Our calculator supports all these applications with multiple interpolation methods. Check our complete FAQ page for more examples.

Complete Guide to Interpolation

Understanding the mathematical techniques behind estimating values from known data points

What is Interpolation?

Interpolation is a mathematical method used to estimate unknown values between known data points. When you have a set of discrete data points, interpolation helps you find values between these points by fitting a continuous function through them.

This technique is particularly useful in science, engineering, and data analysis when you need to:

  • Estimate missing values in a dataset
  • Create a smooth curve from discrete measurements
  • Predict intermediate values for complex systems
  • Visualize trends in experimental data

For more detailed information about interpolation applications, visit our FAQ page, which explains common use cases in different industries.

Interpolation Methods

Our calculator offers three interpolation methods, each with unique advantages for different data types. Check our step-by-step tutorial for detailed examples.

Linear Interpolation

The simplest form of interpolation, connecting points with straight lines. Quick to calculate and easy to understand, ideal for relatively linear data.

Pros:
  • Simple and intuitive
  • Computationally fast
  • Stable with all datasets
Cons:
  • Not smooth at data points
  • Less accurate for curved data

Polynomial Interpolation

Uses polynomials of higher degrees to find unknown data. Suitable for data showing non-linear trends. Creates a smooth curve through all points but may oscillate wildly with many points.

Pros:
  • Smooth continuous curve
  • Passes through all points
Cons:
  • May oscillate wildly (Runge's phenomenon)
  • Not suitable for large datasets

Cubic Spline Interpolation

Creates a piecewise function with cubic polynomials between each pair of data points. Provides smoothness and avoids the oscillation problems of high-degree polynomials.

Pros:
  • Smooth at all points
  • Stable with large datasets
  • Minimal oscillation
Cons:
  • More computationally intensive
  • Requires at least 3 points

Note: For most practical applications, cubic spline interpolation provides the best balance between smoothness and accuracy. See our disclaimer for calculation accuracy information.

Real-World Applications

Machine Learning

Used to create multiple data points from a known set, improving model training and prediction accuracy.

Computer Graphics

Resizes images, creates smooth animations, and enables motion tracking in 3D graphics applications.

Scientific Research

Essential for analyzing experimental data, creating mathematical models, and predicting outcomes in research.

Explore more applications

How to Choose the Right Method

Selecting the appropriate interpolation method depends on your data characteristics and requirements:

When to Use Linear Interpolation

  • Data points appear to follow straight lines
  • Simple, quick estimation is needed
  • Working with just a few data points
  • Computational efficiency is important

When to Use Cubic Spline Interpolation

  • Smooth curves are required
  • Working with larger datasets
  • Need to avoid oscillation issues
  • Data represents natural phenomena

When to Avoid Polynomial Interpolation

High-degree polynomial interpolation can produce unexpected results:

  • With many data points (> 10), as wild oscillations may occur
  • When extrapolating beyond the data range
  • For noisy data with measurement errors
Learn more about method selection in our FAQ

Common Challenges & Solutions

Runge's Phenomenon

The Problem

High-degree polynomial interpolation can lead to wild oscillations between data points.

The Solution

Use cubic spline interpolation instead, which creates piecewise polynomials of lower degree.

Best Practice

For datasets with more than 10 points, use cubic spline interpolation for more stable results.

Data Point Selection

The Problem

Too few data points can miss crucial behavior in the underlying function.

The Solution

Include more data points in regions of high curvature or rapid change.

Best Practice

Try different methods and compare the results visually to find the best fit for your data.

Calculation Accuracy

The Problem

Floating-point arithmetic can introduce small errors in calculation results.

Our Solution

Our calculator guides you to select the right method and validates results automatically.

Read our full disclaimer on calculation accuracy

Ready to start interpolating your data?

Our calculator makes it easy to get accurate results fast. Try it now!

Start Calculating NowView Tutorial