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Linear Interpolation Between Two Points Calculator (Step by Step with Example)

📈 Have you ever needed to estimate a value between two known points on a graph or dataset? That’s exactly what linear interpolation is for. It’s a quick and reliable way to find missing values between two known data points by assuming a straight-line relationship between them.

In this article, you’ll learn what linear interpolation is, how to calculate it, and when to use it—with an easy-to-follow example.

🙋 What Is Linear Interpolation?

Linear interpolation is a method of estimating an unknown value that lies between two known values. It assumes the data points lie on a straight line and uses that line to fill in the gaps.

It’s commonly used in:

  • Physics and engineering
  • Finance and economics
  • Data science and statistics
  • Everyday problem solving

🧮 The Formula

If you know two points:

  • (x0, y0)
  • (x1, y1)

You can estimate the value of y for any x between x0 and x1​ using the formula:

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

This calculates the slope of the line between the two points and applies it to estimate the new value.

Try the calculator below. Enter 5 values x0, y0, x1, y1, x to find y

⚙️ Linear Interpolation Calculator













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✅ When to Use It

Use linear interpolation when:

  • You have two known data points
  • You want to estimate a value between them
  • You assume the data behaves linearly (like a straight line)

Linear interpolation is not ideal for data with curves or sudden changes—it’s best for predictable, gradual trends.

🧑‍🏫 Example: Estimating Temperature

Let’s say you’re tracking temperature and have the following data:

  • At 8 AM, the temperature was 15°C → (x₀ = 8, y₀ = 15)
  • At 10 AM, the temperature was 25°C → (x₁ = 10, y₁ = 25)

Now, you want to estimate the temperature at 9 AM (x = 9).

Using the formula:

y = 15 + (9 – 8) * (25 – 15) / (10 – 8)
y = 15 + (1) * (10) / (2)
y = 15 + 5
y = 20

So, the estimated temperature at 9 AM is 20°C.

📌 Why It Matters

Linear interpolation is:

  • Simple to use
  • Quick to calculate
  • Widely used across industries
  • Great for real-time data estimation

It’s a basic but powerful tool for estimating unknown values using only two points.

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