📐 Numerical Analysis & Linear Estimation
Linear & Bilinear Interpolation (LERP) Calculator
Estimate unknown values between two known boundary coordinates ($x_1, y_1$) and ($x_2, y_2$), compute normalized parameter $t$, slope rate ($m$), and flag extrapolation warnings.
Known Boundary Points
x₁
y₁
x₂
y₂
Interpolated Value y
y = 70.000
Parameter ($t$)
0.500 (50.0%)
Slope Rate ($m$)
+4.000
Y-Intercept ($b$)
10.000
💡 Linear Equation:
$$y = 50 + \frac{90 - 50}{20 - 10} \times (15 - 10) = 50 + (4.0 \times 5) = 70.0$$
The Linear Interpolation Formula
Assuming linear behavior between two discrete data points:
$$y = y_1 + \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) = (1 - t)y_1 + t y_2, \quad t = \frac{x - x_1}{x_2 - x_1}$$
- Interpolation ($0 \le t \le 1$): The target $x$ lies within the known boundary window $[x_1, x_2]$.
- Extrapolation ($t < 0$ or $t > 1$): The target $x$ lies outside the known range, carrying increased uncertainty.