What types of 3D functions can I graph?

You can graph functions of two variables like z = f(x,y), including surfaces, paraboloids, saddle points, and more. Examples: x^2 + y^2, sin(x)*cos(y), x^2 - y^2.

How do I navigate the 3D graph?

Click and drag to rotate the 3D view, use scroll wheel to zoom in/out, and use the control buttons for preset views and animations.

Can I plot multiple 3D functions simultaneously?

Yes, you can plot up to 3 different 3D surfaces simultaneously with different colors and transparency levels for comparison.

📊 3D Graph Calculator

3D Functions (z = f(x,y))

f₁(x,y) =

f₂(x,y) =

f₃(x,y) =

X Range

Y Range

Quality

What is a 3D Graph Calculator?
This advanced 3D graphing tool allows you to visualize functions of two variables (z = f(x,y)), creating interactive 3D surfaces. Perfect for multivariable calculus, surface analysis, and advanced mathematical visualization.

3D Function Analysis Features

Interactive 3D Visualization: Rotate, zoom, and explore 3D surfaces with mouse controls.
Multiple Functions: Plot up to 3 different functions simultaneously with color coding.
Critical Points: Find maximum, minimum, and saddle points automatically.
Surface Analysis: Calculate gradients, partial derivatives, and surface metrics.
Point Evaluation: Get function values at specific (x,y) coordinates.

Example: Enter x^2 + y^2 to plot a paraboloid, or sin(x)*cos(y) for a wave surface.

3D Graph View

Current Analysis

Status

Ready to plot 3D functions

Quick Examples

Related Math Calculators

How to Use the 3D Graph Calculator

Enter 3D Functions: Type functions of two variables using x and y (e.g., x^2 + y^2, sin(x)*cos(y)).
Navigate in 3D: Click and drag to rotate the view, scroll to zoom, use control buttons for preset views.
Adjust Parameters: Set X/Y ranges and resolution for optimal visualization.
Multiple Functions: Plot up to 3 different surfaces with color coding.
Quick Examples: Use the example buttons to explore different types of 3D surfaces.
Export: Save your 3D graphs as images for presentations or reports.

Supported 3D Function Types

Basic 3D Functions

Quadratic Surfaces: x^2 + y^2, x^2 - y^2, x*y
Polynomial: x^3 + y^3, x^2*y + x*y^2
Linear Planes: x + y, 2*x - 3*y + 5
Exponential: e^(x+y), e^(x^2+y^2), e^(-x^2-y^2)

Advanced 3D Functions

Trigonometric: sin(x)*cos(y), sin(x+y), cos(x^2+y^2)
Logarithmic: ln(x^2+y^2), log(abs(x)+abs(y))
Combined: x^2*sin(y), e^(-x^2)*cos(y)
Special Surfaces: sqrt(x^2+y^2), abs(x)+abs(y)

Real-Life 3D Applications

Engineering & Physics

Temperature Distribution: Model heat distribution across a surface
Electromagnetic Fields: Visualize field strength in 3D space
Stress Analysis: Plot material stress across 2D surfaces
Wave Propagation: Model sound or water waves in 2D

Economics & Business

Profit Optimization: Find optimal pricing and production levels
Cost Surfaces: Model costs based on two variables
Risk Analysis: Visualize risk across different scenarios
Market Analysis: Plot demand as function of price and quantity

3D Features

Plot up to 3 3D surfaces simultaneously
Interactive 3D rotation and zoom
Wireframe and surface rendering modes
Adjustable transparency and resolution
Real-time function evaluation

Critical point and saddle point analysis
Gradient and contour visualization
Volume calculation under surfaces
Export to high-quality images
Responsive design for all devices

Frequently Asked Questions

You can graph functions of two variables (z = f(x,y)) including:

Quadratic surfaces: x^2 + y^2 (paraboloid), x^2 - y^2 (saddle)
Trigonometric surfaces: sin(x)*cos(y), sin(x+y)
Exponential surfaces: e^(x+y), e^(-(x^2+y^2))
Complex surfaces: x^2*y + y^3, sqrt(x^2+y^2)

Use x and y as your variables, and the calculator will plot the resulting z values.

Rotate: Click and drag to rotate the 3D view
Zoom: Use scroll wheel or pinch gestures to zoom in/out
Pan: Hold shift and drag to pan the view
Reset: Click "Reset View" to return to default orientation
Auto Rotate: Enable automatic rotation for presentations

Critical Points: Find maxima, minima, and stationary points
Saddle Points: Identify saddle points where the surface curves differently
Gradient: Calculate and visualize the gradient vector field
Volume: Compute volume under the surface within specified bounds
Contour Analysis: Generate and analyze level curves

Yes! You can plot up to 3 different 3D surfaces simultaneously:

Each function has its own color (blue, green, red)
Adjust opacity to see overlapping surfaces
Toggle individual functions on/off
Compare different mathematical relationships
Analyze intersections between surfaces