Linear Extrapolation Calculator (with Examples and Formula)

📈 Linear extrapolation is a powerful method used to estimate values outside a known data range using a straight-line projection. Whether you’re analyzing trends in business, predicting engineering results, or forecasting future data, this technique is fast, simple, and widely used.

In this article, we’ll explain what linear extrapolation is, how it works, and give you a handy calculator to use directly on your site.

🙋‍♀️ What Is Linear Extrapolation?

Linear extrapolation is the process of estimating a new data point by extending a straight line between two known points beyond the known range.

If you know two data points:

  • (x₀, y₀)
  • (x₁, y₁)

You can estimate y at a new x value outside the interval [x₀, x₁] using the same slope.

Use the calculator below to compute extrapolated values from any two known points:

👉 Enter two known points and a new x-value to calculate y!

🧮 Linear Extrapolation Calculator













Powered by onesdr.com

✏️ Formula for Linear Extrapolation

The formula used is:

y = y₀ + ((x – x₀) * (y₁ – y₀)) / (x₁ – x₀)

Where:

  • x is the point at which you want to extrapolate
  • x₀ and x₁ are the known x-values
  • y₀ and y₁ are the corresponding y-values

This is the same formula used in linear interpolation, but instead of estimating within the known range, you use it outside that range.

⏩ When to Use Linear Extrapolation

  • Forecasting revenue or population growth
  • Predicting stock prices based on past trends
  • Engineering applications where trends continue beyond measured points
  • Estimating sensor readings or data in embedded systems

⚙️ Example Calculation

Let’s say we know two points:

  • (2, 50)
  • (4, 70)

Now, you want to extrapolate for x = 6.

Using the formula:

y = 50 + ((6 – 2) * (70 – 50)) / (4 – 2)
y = 50 + (4 * 20) / 2
y = 50 + 80 / 2
y = 50 + 40
y = 90

So the extrapolated value at x = 6 is 90.

💡 Final Thoughts

Linear extrapolation is a fast and easy way to predict future data, but be cautious when using it. The further you extrapolate from your known points, the greater the risk of inaccuracy. Trends can change suddenly, and a straight line may not always represent reality.

For small extensions or linearly trending data, however, it’s incredibly useful.

🔁 Related Posts