Vector Fields (quiver & streamplot)

A vector field plot draws an arrow at each point in a grid to show direction and strength, letting you visualize forces, winds, currents, or any quantity that has both a magnitude and a heading.

Learn Vector Fields (quiver & streamplot) in our free Matplotlib course — a beginner-friendly interactive lesson with worked examples, a practice exercise…

Part of the free Matplotlib course at LearnCodingFast — hands-on lessons with examples you run in your browser, plus practice exercises and a quick quiz.

In this lesson you'll build arrow grids with ax.quiver() , trace smooth flow lines with ax.streamplot() , control arrow scale and line density, and color both by magnitude.

A quiver plot needs four ingredients: the X and Y positions of each arrow and the U and V components of the vector at that position. U is how far the arrow points along x, V is how far along y. You almost always build the positions with np.meshgrid() , which turns two 1-D ranges into a full 2-D grid of coordinates.

What you'll see: a 6×6 grid of blue arrows that curl counter-clockwise around the center — short near the middle and longer toward the edges — because the field U = −Y, V = X gets stronger the farther you move from the origin.

By default Matplotlib auto-scales arrow length to fit the axes. Pass scale to take control: a larger scale makes arrows shorter, a smaller scale makes them longer. To color arrows by strength, compute the magnitude with np.sqrt(U**2 + V**2) and pass it as the fifth argument — Matplotlib runs it through a colormap.

Where quiver shows discrete arrows, ax.streamplot() traces the continuous paths a particle would follow through the field. It takes the same X, Y, U, V data but draws smooth curves with little arrowheads. Use density to pack in more or fewer lines, and pass an array to color to tint the streamlines by magnitude.

What you'll see: smooth concentric loops swirling around the center, each carrying a tiny arrowhead, tinted from cool blue near the calm middle to brighter colors where the flow speeds up at the edges.

Replace each ___ to draw a quiver field of a uniform wind blowing up and to the right.

Your scale is too high, so arrows are shrunk to nothing. ✅ Lower the scale, or drop the argument entirely and let Matplotlib auto-scale.

❌ streamplot: "The rows of 'x' must be equal"

streamplot needs an evenly spaced, strictly increasing grid. ✅ Build X and Y with np.linspace + np.meshgrid , not hand-typed lists.

U and V must have the same 2-D shape as X and Y. ✅ Derive U and V from X and Y (e.g. U = -Y ) so the shapes always line up.

Overlay a coarse quiver field on top of fine streamlines of the same vortex, so you see both the individual arrows and the overall flow.

Lesson complete — you can visualize vector fields!

You built coordinate grids with meshgrid, drew arrow fields with quiver, scaled them and colored them by magnitude, and traced smooth flow lines with streamplot.

🚀 Up next: Customizing Spines — hide, move, and restyle the axis borders for a clean, minimalist look.

Practice quiz

• Browse all free courses
• Cheat sheets & quizzes
• Coding dictionary