Model surfaces using flexible equations and instant results. Compare gradients, tables, charts, and downloadable reports. Built for students, analysts, and quick everyday math checks.
This page stays in a single vertical flow. The calculator grid adapts across screen sizes.
| Time | Model | x | y | z | ∂z/∂x | ∂z/∂y | |∇z| |
|---|---|---|---|---|---|---|---|
| No calculations yet. Submit the form to build history. | |||||||
Sample interaction model: z = 2 + 1.2x + 0.8y + 0.3xy
| Row | x | y | Calculated z |
|---|---|---|---|
| 1 | 1.0 | 1.0 | 4.3 |
| 2 | 2.0 | 1.0 | 5.8 |
| 3 | 2.0 | 2.0 | 7.2 |
| 4 | 3.0 | 1.5 | 8.15 |
| 5 | 4.0 | 2.0 | 10.8 |
Linear plane: z = a + bx + cy
Interaction surface: z = a + bx + cy + dxy
Quadratic surface: z = a + bx + cy + dx² + ey² + fxy
Exponential surface: z = a · e^(bx + cy)
Partial derivative with respect to x: Measures how z changes when only x changes.
Partial derivative with respect to y: Measures how z changes when only y changes.
Gradient magnitude: |∇z| = √[(∂z/∂x)² + (∂z/∂y)²]
Tangent plane: A local linear estimate around the selected point.
It evaluates a bivariate function where z depends on x and y. It also estimates local change using partial derivatives and gradient magnitude.
Use the linear plane for simple relationships. Use interaction when x and y influence each other. Use quadratic for curvature. Use exponential for rapid growth or decay.
Different models use different terms. For example, the plane uses only a, b, and c. Extra coefficients are ignored when the model does not need them.
They show the rate of change at the chosen point. ∂z/∂x changes x only. ∂z/∂y changes y only.
It summarizes how steep the surface is at the selected point. Larger values mean z changes faster near that location.
The graph is redrawn over your selected x and y window. Wider ranges reveal global shape. Tighter ranges highlight local surface behavior.
It is useful for local approximation. Near the chosen point, the tangent plane estimates nearby z values using a simple linear form.
Yes. It works well for multivariable practice, model testing, quick verification, and illustrating how coefficients reshape a surface.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.