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Linear Interpolation Calculator

Enter the required values in their respective fields, and the tool will determine their interpolated values, with step-by-step computations shown

Enter the five values below to find the linear interpolation

x₁:

y₁:

x₂:

y₂:

x₃:

y₃:

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Linear Interpolation Calculator

An online linear interpolation calculator helps find interpolated values for data points on a line or curve. The calculator plots the interpolated point and provides a step-by-step solution using the linear interpolation formula.

What is Linear Interpolation?

Linear interpolation estimates new data points within a set of known discrete points. A linear interpolant is a straight line connecting two known coordinates \((x_1, y_1)\) and \((x_2, y_2)\). The interpolated value is calculated using this line.

Linear Interpolation Formula:

\[ y = y_1 + \frac{(x - x_1)}{(x_2 - x_1)} \cdot (y_2 - y_1) \]

Where:

x = known value
y = interpolated value
(x1, y1) = coordinates below the known x
(x2, y2) = coordinates above the known x

Linear Interpolation Example

An Online Slope Calculator can also help find slopes between points.

Example 1

Given points \((2, 4)\) and \((6, 8)\), find y when x = 2:

Extract coordinates: \(x_1=2, y_1=4, x_2=6, y_2=8\)
Calculate slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-4}{6-2} = 1 \]
Use the formula: \[ y = y_1 + m(x - x_1) = 4 + 1(2 - 2) = 4 \]

This is a valid linear interpolation since x lies within [x1, x2].

Example 2

Find \(y_2\) using points \(x_1 = 4, y_1 = 6, x_2 = 8, x_3 = 12, y_3 = 14\).

Linear interpolation formula:

\[ y_2 = y_1 + \frac{(x_2 - x_1)(y_3 - y_1)}{(x_3 - x_1)} \]

Step-by-step calculation:

\[ y_2 = 6 + \frac{(8 - 4)(14 - 6)}{12 - 4} = 6 + \frac{4 \cdot 8}{8} = 6 + 4 = 10 \]

An Online Centroid Calculator can also help with coordinates for triangles and polygons.

How the Linear Interpolation Calculator Works

Input:

Enter data points (up to 5 or more) to interpolate a specific point.
Click the Calculate button.

Output:

Interpolated value at the specified point
Plot of the interpolated point on a line
Input data points and linear interpolation formula
Step-by-step solution for the interpolated value

Frequently Asked Questions (FAQs)

Which method can be used in any interpolation question?

Polynomial interpolation is widely used because it is easy to evaluate, differentiate, and integrate.

When should interpolation be used?

Interpolation predicts unknown values within a set of known points, e.g., rainfall, chemical concentrations, or noise levels.

Which is the best interpolation method?

Inverse Distance Weighted (IDW) interpolation is highly accurate for many datasets.

Is Kriging an exact interpolation?

Kriging is generally exact; predictions can adjust as new data points are added.

Conclusion

The linear interpolation calculator quickly finds unknown values for given coordinates, plots them on a graph, and provides step-by-step calculations for educational and practical purposes.

References

Wikipedia: Linear interpolation
Science Direct: Linear Interpolation Methods
Dagra: Linear Interpolation Equations

Other Languages: Kalkulator Interpolasi, Interpolacja Kalkulator, Interpolation Rechner, Interpolasyon Hesaplama, 補間計算, Calculadora De Interpolação, Calcul Interpolation Linéaire, Interpolar Calculadora, Calcolo Interpolazione Lineare, Калькулятор Интерполяции, Lineární Interpolace Výpočet, حاسبة الاستيفاء, Interpolointi Laskin.

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