Contour Plot Calculator for Machine Learning

Results

Ready to calculate.

Minimum Z

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Maximum Z

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Mean Z

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Grid cells

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Minimum location

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Maximum location

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Standard deviation

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Missing cells

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Level	Cells ≤ level	Surface share	Status
Generate a plot to see contour statistics.

Interpretation

Contour lines connect points with equal values. Generate a plot to view a tailored interpretation.

Validation

No validation issues.

1. Data source and function

Data source

Example preset

Primary function, z = f(x,y)

Use math.js syntax. Supported examples include sin(x), cos(y), exp(), sqrt(), abs(), log(), pi, and powers with ^.

Secondary function for comparison

Comparison mode

Import CSV

CSV delimiter

2. Grid, range, and interpolation

X minimum

X maximum

Y minimum

Y maximum

X resolution

Y resolution

Random seed

Noise level

3. Data transformations

Transformation

Clip minimum

Clip maximum

Outlier Z threshold

Set zero to keep all values.

4. Contour levels and display

Plot type

Level mode

Level start

Level end

Level count

Custom levels

Comma-separated levels. Each level can be drawn separately.

Zero contour

Colour scale

Reverse colour scale

Filled opacity0.90

Contour line width

Contour line colour

Contour labels

Colour bar

Colour bar orientation

Colour bar title

Tick precision

Number format

5. Titles, axes, and layout

Plot title

Subtitle

X-axis title

Y-axis title

X-axis scale

Y-axis scale

Aspect ratio

Reverse X axis

Reverse Y axis

Grid lines

Zero lines

Font size

Plot height

3D surface view

6. Machine learning overlays

Input points

Point size

Minimum and maximum

Gradient arrows

Gradient density

Gradient arrow scale

Decision boundary level

Decision boundary

7. Gradient-descent simulator

Optimization path

Start X

Start Y

Learning rate

Iterations

Momentum

Tolerance

Optimizer

Path animation

8. Saved settings and export

Settings name

Saved configurations

Formula used

A contour line contains coordinates sharing one function value. It satisfies f(x,y) = c, where c is a selected level.

The numerical gradient is estimated from nearby values. Gradient descent updates both coordinates opposite the local gradient direction.

∇f(x,y) = [∂f/∂x, ∂f/∂y]
x(t+1) = x(t) - η ∂f/∂x
y(t+1) = y(t) - η ∂f/∂y

How to use

Select a function, grid, scattered dataset, or synthetic source.
Choose ranges, resolution, interpolation, and transformations.
Configure contour levels, colours, axes, and optional overlays.
Enable gradient descent to inspect an optimization path.
Generate the chart, review statistics, and export results.

Example data

Use case	X	Y	Z	Interpretation
Loss landscape	Parameter one	Parameter two	Loss	Lower contours indicate preferred parameter regions.
Hyperparameter search	Learning rate	Regularization	Validation score	Higher contours indicate stronger model performance.
Decision surface	Feature one	Feature two	Class probability	The 0.5 contour can represent a decision boundary.

Frequently asked questions

What does a contour line show?

It connects points having the same Z value. Closely spaced contours usually indicate rapid change.

Can I use scattered data?

Yes. The calculator interpolates scattered points onto a regular grid before plotting.

Which interpolation method should I choose?

Nearest neighbour preserves local samples. IDW and radial methods create smoother estimated surfaces.

How do contours help machine learning?

They reveal loss minima, parameter interactions, decision boundaries, confidence regions, and hyperparameter performance.

Why are some cells missing?

A function may be undefined there. Masking or outlier removal can also create missing cells.

What is a good grid resolution?

Start near eighty points per axis. Increase resolution carefully for smoother contours.

Can the calculator find a minimum?

It identifies the lowest sampled cell. The optimization simulator can also trace a local descent path.

How is the gradient calculated?

The calculator uses central finite differences where possible. Edge points use one-sided approximations.

Can I export the complete analysis?

Yes. Export images, CSV data, contour levels, JSON settings, copied results, or a PDF report.

Contour Plot Calculator