Interpolation and Extrapolation Calculator

Linear Formula:

\[ Y = Y_1 + (X - X_1) \times \frac{Y_2 - Y_1}{X_2 - X_1} \]

Calculated Y:

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1. What is Interpolation and Extrapolation?

Interpolation is the process of estimating unknown values that fall between known data points, while extrapolation extends this estimation beyond the known data range. Linear interpolation assumes a straight-line relationship between data points.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

\[ Y = Y_1 + (X - X_1) \times \frac{Y_2 - Y_1}{X_2 - X_1} \]

Where:

\( X_1, Y_1 \) — First known data point
\( X_2, Y_2 \) — Second known data point
\( X \) — Input X value for which to estimate Y
\( Y \) — Calculated output value

Explanation: This formula calculates the Y-value corresponding to a given X-value by assuming a linear relationship between two known data points.

3. Applications of Linear Interpolation

Details: Linear interpolation is widely used in mathematics, engineering, computer graphics, finance, and scientific research to estimate values between known data points without knowing the exact function relationship.

4. Using the Calculator

Tips: Enter two known data points (X1,Y1) and (X2,Y2), then input the X value for which you want to estimate Y. The calculator will return the interpolated or extrapolated Y value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between interpolation and extrapolation?
A: Interpolation estimates values within the range of known data points, while extrapolation estimates values outside this range.

Q2: When is linear interpolation appropriate?
A: When the relationship between variables is known to be linear or approximately linear between the data points.

Q3: What are the limitations of linear interpolation?
A: It assumes a straight-line relationship, which may not accurately represent nonlinear relationships. Accuracy decreases with greater distance from known points.

Q4: Can I use this for extrapolation far beyond my data points?
A: While mathematically possible, extrapolation far beyond known data becomes increasingly unreliable as it assumes the linear relationship continues indefinitely.

Q5: What if my X1 and X2 values are the same?
A: The calculation is undefined when X1 = X2 (division by zero). You need distinct X values for linear interpolation.