When working with data, graphs, or trends, you might hear two terms thrown around a lot: interpolation and extrapolation. While they sound similar, they do different things. Let’s break it down in a simple way. We’ve also included a calculator that you can experiment with ✨
Table of Contents
🙋♀️ What is Interpolation?
Interpolation is like filling in the blanks within known data points.
Imagine you’re looking at a graph showing the temperature at 8 AM, 10 AM, and 12 PM. If you want to know the temperature at 9 AM, you’d use interpolation. You’re staying inside the known range.
Example
You know:
- At 8 AM, it’s 15°C
- At 10 AM, it’s 19°C
You can use interpolation to estimate the temperature at 9 AM, assuming the temperature rises steadily.
In a nutshell
- Interpolation works inside the known data range
- It’s generally more accurate because it uses nearby data
- Used in science, finance, engineering, and more
🙋 What is Extrapolation?
Extrapolation is predicting what comes outside the known data.
Using the same temperature example, if you want to estimate the temperature at 1 PM, you’d be extrapolating. You’re guessing beyond what you already know.
Example:
You have:
- 10 AM: 19°C
- 12 PM: 23°C
You want to guess the temperature at 1 PM — that’s extrapolation. You assume the trend continues beyond the known time.
In a nutshell:
- Extrapolation works outside the known data range
- It’s riskier because trends can change
- Still useful in forecasting, projections, and predictions
🔀 Key Differences
| Feature | Interpolation | Extrapolation |
|---|---|---|
| Works within range | ✅ Yes | ❌ No |
| Works outside range | ❌ No | ✅ Yes |
| Accuracy | High (usually) | Lower (depends on the situation) |
| Common uses | Estimating missing data | Predicting future or unknown values |
| Risk | Low | Higher |
🛠️ When Should You Use Each?
- Use interpolation when your target value lies between known data points
- Use extrapolation when your target value is outside the known data range
🌐 Real-World Examples
Interpolation:
- Estimating a student’s grade on a test if you know their average score from similar exams
- Filling in a missing sensor reading in a temperature log
Extrapolation:
- Forecasting next year’s revenue based on past growth
- Predicting population in 2030 using census data from previous years
🧪 Example Use Case
If you enter:
- x₁ = 2, y₁ = 4
- x₂ = 6, y₂ = 12
- x = 4
You’ll get: Interpolation Result: y = 8.00
If you change x to 8, you’ll get: Extrapolation Result: y = 16.00
🎯 Final Thoughts
Both interpolation and extrapolation are helpful tools in data analysis. Interpolation tends to be more reliable because it stays within familiar territory, while extrapolation can help you predict the future — but it comes with more risk.
Use them wisely, and they can turn numbers into powerful insights!