Linear Interpolation Calculator
Visualize and calculate linear relationships with precision
Input Values
Graph Visualization
1. Instant & Accurate Calculations
The formulae in the tool provide the standard linear interpolation formula to provide mathematical accuracy at all times.
Interactive Graph Visualisation
Every point, including that which you have interpolated.
3. Step-by-Step Formula Display
Get to the point and see how it is calculated.
4. Copy & Export Results Easily
Rapidly duplicate the interpolated y-value, slope, or complete calculation.
Linear interpolation is a simple mathematical process of estimating a value or number between two known data.
It supposes that change between the points is straight (in a straight line).
Here:
- (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) are known points.
- xxx is the target value
- yyy is the interpolated value
To put it simply, it makes predictions of in-between values where the relationship between the points of data is a straight line.
Example 1: Temperature Estimation
You wish to know the temperature at 5 AM, having the following amount of data:
- At 2 AM, temperature = 10°C
- At 8 AM, temperature = 22°C
Result:
- The estimated temperature at 5 AM is 16°C.
Example 2: Financial Growth Projection
- A company’s revenue was
- $100,000 in 2020
- $200,000 in 2025.
- Estimate the revenue for 2023 using linear interpolation.
- Result:
- The projected revenue for 2023 is $160,000.
Example Calculations
| Example | x₁ | y₁ | x₂ | y₂ | Target x | Interpolated y |
|---|---|---|---|---|---|---|
| Temperature Estimation | 0 | 30°C | 10 | 50°C | 5 | 40°C |
| Finance Projection | 2020 | 100 | 2025 | 200 | 2022 | 140 |
| Engineering Measurement | 2 | 4 | 8 | 16 | 5 | 10 |
- In the last example, when x = 5, y=4+(5−2)×(16−4)/(8−2)=10y = 4 + (5 – 2) × (16 – 4) / (8 – 2) = 10y=4+(5−2)×(16−4)/(8−2)=10
Linear Interpolation:
Linear Interpolation has the following applications.
- Geographic Data: Estimate elevation or location between coordinates.
- Engineering: Estimate missing data points in experiments.
- Finance: Predict the intermediate between fiscal years.
- Science: Approximate pressure, temperature, or velocity at specific points.
- Data Analysis: Interpolate the missing values between known data values.
Estimate elevation or location between coordinates.
