Enter field functions, ranges, density, and scaling for plotting. Evaluate vectors at chosen points accurately. Review field behavior, slope flow, and local strength clearly.
A two-dimensional vector field is written as F(x,y) = <P(x,y), Q(x,y)>.
The vector at a chosen point is F(x0,y0) = <P(x0,y0), Q(x0,y0)>.
The magnitude is |F| = sqrt(P² + Q²).
The direction angle is atan2(Q, P).
Approximate divergence is dP/dx + dQ/dy.
Approximate curl in two dimensions is dQ/dx - dP/dy.
The graph samples many grid points, then draws an arrow at each point.
| x | y | P(x,y) | Q(x,y) | Magnitude |
|---|---|---|---|---|
| -2 | -2 | 2 | -2 | 2.8284 |
| -1 | 0 | 0 | -1 | 1.0000 |
| 0 | 1 | -1 | 0 | 1.0000 |
| 1 | 2 | -2 | 1 | 2.2361 |
| 2 | 2 | -2 | 2 | 2.8284 |
A vector field graph calculator helps you study how a field behaves across a plane. This page plots arrows from two component functions. Each arrow shows direction and strength at one coordinate pair. That makes patterns easy to inspect. You can test flow, growth, rotation, and local movement in one view.
This calculator is useful for calculus, differential equations, physics, and engineering work. Students can compare fields before solving a system. Teachers can create fast examples for class. Analysts can inspect gradients, motion rules, and directional changes without drawing every arrow by hand.
A plotted field reveals structure quickly. You can spot symmetry, sinks, sources, shear, and rotation. A table alone does not show that shape clearly. The graph helps you connect equations with geometry. It also shows how magnitude changes from point to point.
The evaluation section adds more depth. It calculates the vector at a selected point, the magnitude, the angle, approximate divergence, and approximate curl. These values help explain whether the field spreads outward, compresses inward, or rotates around a location.
Use this tool to inspect slope flow in planar systems. Check a gradient-style field. Review a motion model in two dimensions. Compare normalized arrows with magnitude-based arrows. Adjust the grid density when you need either a quick overview or more detail.
The export options also help. CSV output gives reusable coordinate data for reports or spreadsheets. PDF export creates a clean snapshot for notes, assignments, or client files. That saves time when you need both visualization and documentation.
The layout stays simple and readable. The result appears above the form after calculation. The graph, summary values, and preview table stay together. That keeps the workflow clear. Enter functions, set the range, plot the field, and review the computed values. It is a practical way to study two-variable vector behavior with less manual effort.
You can also compare different ranges and step densities to see how sampling changes the picture. A coarse grid is fast. A dense grid is richer. That balance matters when you study local detail and global trends together.
It shows an arrow at each sampled coordinate. The arrow direction follows the field direction. The arrow length can represent either normalized direction or local magnitude.
You can use x, y, numbers, parentheses, and common math functions. Examples include sin, cos, tan, sqrt, abs, exp, log, ln, min, max, and powers with ^.
Normalized arrows focus on direction. They use nearly equal arrow lengths. Scaled arrows use magnitude, so stronger regions appear with longer arrows and weaker regions appear shorter.
They add local insight. Divergence estimates outward or inward spreading. Curl estimates local rotation. Together, they help explain the behavior of the field near the chosen point.
Start with a medium density such as 11. Increase it for more detail. Lower it when you want a cleaner overview or faster processing on large ranges.
Yes. It is useful for planar systems and direction analysis. You can inspect how the field behaves before solving trajectories or comparing equilibrium behavior.
The CSV file contains every sampled point in the grid. It includes x, y, the horizontal component, the vertical component, and the computed magnitude.
Reduce the density or shorten the scale. You can also narrow the coordinate range. Those changes make each arrow easier to inspect and compare.
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.