Linear Interpolation Calculator
Find the interpolated value $y$ between two tabulated coordinates $(x_1, y_1)$ and $(x_2, y_2)$ for thermodynamics, steam tables, and engineering data.
What does the Linear Interpolation Calculator do?
The Herramix Linear Interpolation Calculator is a fast utility for mechanical, chemical, civil, and electrical engineers who regularly look up intermediate values in thermodynamic steam tables, psychrometric charts, air property tables, or experimental datasets.
Enter the upper table row as $(x_1, y_1)$ and the lower row as $(x_2, y_2)$, then type your target $x$. The calculator immediately computes $y$ along with the interval slope $m$ and linear equation:
\[ y = y_1 + \frac{x - x_1}{x_2 - x_1} \cdot (y_2 - y_1) \]Usage example
Scenario (Steam tables): At $x_1 = 100\text{ }^\circ\text{C}$, saturated steam enthalpy is $y_1 = 2675.6\text{ kJ/kg}$, and at $x_2 = 120\text{ }^\circ\text{C}$ it is $y_2 = 2706.0\text{ kJ/kg}$. Find the enthalpy at $x = 112\text{ }^\circ\text{C}$.
Result: $y = 2693.84\text{ kJ/kg}$ (60% of the way between $100\text{ }^\circ\text{C}$ and $120\text{ }^\circ\text{C}$).
Frequently Asked Questions
What happens if $x_1$ and $x_2$ are equal?
If $x_1 = x_2$, the denominator $(x_2 - x_1)$ becomes zero (a vertical line), so $x_1$ and $x_2$ must be two distinct coordinates.
Can I use this tool for linear extrapolation?
Yes. Entering an $x$ value smaller than $x_1$ or larger than $x_2$ automatically projects the line slope to return the linearly extrapolated $y$ value.
When is linear interpolation accurate enough?
Linear interpolation is highly accurate whenever the step size between $x_1$ and $x_2$ is small enough that the underlying curve behaves nearly linearly across the interval.