1. What is Linear Interpolation?

Linear interpolation is a method of estimating values between two known values. It assumes the change between the points is linear and calculates intermediate values accordingly.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

Where:

• \( x \) — The known x-value between x1 and x2
• \( x1, x2 \) — The lower and upper x-boundaries
• \( y1, y2 \) — The corresponding y-values at x1 and x2
• \( y \) — The interpolated y-value at x

Explanation: The formula calculates the slope between two known points and applies this slope to estimate the y-value at any intermediate x-value.

3. Applications of Linear Interpolation

Details: Linear interpolation is widely used in mathematics, computer graphics, engineering, and scientific data analysis to estimate values between measured data points.

4. Using the Calculator

Tips: Enter all known values (x, x1, x2, y1, y2). Ensure x is between x1 and x2 for best results. The calculator will prevent division by zero if x1 equals x2.

5. Frequently Asked Questions (FAQ)

Q1: What if my x-value is outside the x1-x2 range?
A: This is called extrapolation rather than interpolation. Results may be less accurate as they extend beyond known data points.

Q2: When is linear interpolation not appropriate?
A: When the relationship between variables is known to be non-linear (exponential, logarithmic, etc.), other interpolation methods may be better.

Q3: How accurate is linear interpolation?
A: It's perfectly accurate for truly linear relationships. For non-linear relationships, accuracy decreases with the distance between points.

Q4: Can I use this for time-series data?
A: Yes, linear interpolation is commonly used to estimate values between time-based measurements.

Q5: What are alternatives to linear interpolation?
A: Polynomial interpolation, spline interpolation, or nearest-neighbor interpolation may be used depending on the data characteristics.