Map contours and iso-value relationships with clarity. Use flexible inputs for equations, constants, checks, reports. Study level sets quickly across common multivariable forms today.
Choose a model, enter the target level, supply a test point, and compute the matching level curve or surface.
| Model | Input equation | Level k | Resulting set | Example note |
|---|---|---|---|---|
| Linear 2D | 2x - 3y + 6 | 9 | 2x - 3y = 3 | Produces one straight line. |
| Circle 2D | (x - 1)² + (y + 2)² | 16 | Circle of radius 4 | Center is (1, -2). |
| Ellipse 2D | (x² / 9) + (y² / 4) | 1 | Ellipse with semiaxes 3 and 2 | Closed contour around the origin. |
| Quadratic 2D | x² - y² | 4 | Hyperbola-like curve | Discriminant shows open branches. |
| Sphere 3D | (x - 2)² + y² + z² | 25 | Sphere of radius 5 | Useful for 3D level surfaces. |
A level set is the collection of points where a scalar function equals a chosen constant k. The calculator evaluates f and solves f = k for common models.
A level set is the set of all points where a scalar function takes one fixed value. In two variables it often forms curves, while in three variables it often forms surfaces.
The test point lets you check membership. The calculator evaluates the function at that point and compares the result with k using the tolerance you entered.
Tolerance handles rounding and floating-point limits. A point is accepted when the absolute difference between the function value and k is smaller than the selected tolerance.
The calculator uses the conic discriminant B² - 4AC. Negative values suggest ellipse-like shapes, zero suggests parabola-like behavior, and positive values suggest hyperbola-like behavior.
These models are built from squared distances. If k is negative, no real distance can satisfy the equation, so the level set has no real points.
For circles, ellipses, planes, and spheres, the samples are generated directly from formulas. For the general quadratic model, points are sampled numerically from scanned x-values.
The gradient points in the direction of fastest increase of the function. At regular points, it is perpendicular to the level curve or surface passing through that point.
Yes. Level curves are the mathematical basis of contour maps and iso-value plots. This calculator helps inspect their equations, geometry, and representative coordinates.
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.