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2D Vector Field Plotter - Online Math and Physics

Educational Math math physics plotter vector field
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Controls
Click on the plot to add streamline seeds!
Click anywhere to trace a streamline from that point
|F| ↓
|F| ↑
0.00 Vector Magnitude 1.00

Frequently Asked Questions

What is a 2D Vector Field?

A 2D vector field assigns a vector (with an x-component and y-component) to every point in a two-dimensional plane. Mathematically, it's a function F(x,y) = (Fx(x,y), Fy(x,y)). Vector fields are fundamental in physics for describing phenomena like gravitational fields, electric fields, fluid flow, and magnetic fields.

How do I use this vector field plotter?

Enter mathematical expressions for Fx and Fy using variables x and y. You can use functions like sin(x), cos(y), exp(x), sqrt(x^2+y^2), and constants like pi and e. Use ^ or ** for exponentiation. Adjust ranges, grid density, and arrow scaling using the controls. Click on the plot to add streamline seeds!

What are streamlines?

Streamlines (or flow lines) are curves that are everywhere tangent to the vector field. They represent the paths that massless particles would follow if released into the field. In fluid dynamics, they show flow patterns; in electromagnetism, they represent field lines. Streamlines help visualize the "flow" of the vector field.

What do the colors represent?

The color of each arrow indicates the magnitude (strength) of the vector at that point. Blue represents smaller magnitudes, while red represents larger magnitudes. The color scale ranges from blue (weak) through cyan, green, and yellow to red (strong). This color-coding provides an immediate visual understanding of where the field is strongest.

What are common vector fields in physics?

Common examples include: Gradient fields (conservative forces like gravity), Rotational fields (magnetic fields around currents), Source/Sink fields (electric fields from charges), Uniform fields (constant gravitational field near Earth's surface), and Dipole fields (electric or magnetic dipoles). Try the presets to explore these!

How is the arrow scaling calculated?

By default, arrow lengths are proportional to the vector magnitude at each point, with automatic scaling so the largest arrow fits within the grid cell. You can adjust the scaling factor manually using the Arrow Scale slider, or toggle "Uniform Arrow Length" to show all arrows at the same length (showing only direction, with color still encoding magnitude).

Supported Mathematical Functions & Syntax

Variables: x, y  |  Constants: pi, e  |  Functions: sin(x), cos(x), tan(x), exp(x), log(x), ln(x), sqrt(x), abs(x), atan(x), atan2(y,x), asin(x), acos(x), sinh(x), cosh(x), tanh(x), pow(x,n)  |  Operators: +, -, *, /, ^ or ** (power)  |  Examples: sin(x)*cos(y), x^2-y^2, exp(-(x^2+y^2))

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