Linear Interpolation Calculator
Linear Interpolation Calculator
💡 Linear interpolation estimates values between two known points using a straight line.
Enter two points and a target value to calculate interpolation
Calculate intermediate values between data points with our Linear Interpolation Calculator. Perfect for engineers and analysts. Shows formula, visualization, and step-by-step solution.
What is a Linear Interpolation Calculator?
A Linear Interpolation Calculator estimates values between two known data points using straight-line approximation. Essential for engineers, analysts, and students working with data gaps or needing intermediate values.
The Linear Interpolation Formula
y = y₁ + (x - x₁) × (y₂ - y₁)/(x₂ - x₁)Where:
- (x₁,y₁) and (x₂,y₂) are known points
- x is the target x-value between x₁ and x₂
- y is the calculated intermediate value
How to Use the Calculator
- Enter two known (x,y) data points
- Input the target x (or y for reverse calculation)
- View the interpolated result and visualization
- The chart shows your points and calculated value
Key Terms Explained
- Interpolation: Estimating values within known data range
- Extrapolation: Estimating outside known range (less accurate)
- Data Points: Known (x,y) value pairs
- Slope: Rate of change between points (Δy/Δx)
Formula Source
The formula derives from the slope-intercept equation of a line (y = mx + b), a fundamental concept in algebra and numerical analysis used since the 17th century.
Important Notes
- Only accurate for linear relationships
- Results degrade if points are too far apart
- Extrapolation (beyond input range) increases error
- For non-linear data, consider polynomial interpolation
Frequently Asked Questions
Q: How accurate is linear interpolation?
A: Perfect for linear relationships, approximate for others.
Q: Can I interpolate with uneven x-spacing?
A: Yes! The formula works regardless of x-intervals.
Q: Why does my result look wrong?
A: Check if your data is truly linear - plot it first.
Q: What’s the difference from curve fitting?
A: Interpolation passes through exact points; fitting approximates.
Q: When should I not use this?
A: For highly non-linear data or when derivatives matter.