About This Curl and Divergence Calculator
Vector fields appear in fluid flow, electromagnetism, heat transfer, and many geometry problems. Curl and divergence describe two different local behaviors. Divergence measures how much a field spreads outward from a point. Curl measures local rotation around that point. This calculator estimates both values from the three field components you enter.
The tool uses Cartesian variables x, y, and z. You can write each component with operators and common functions. Use multiplication signs between terms. For example, write 2*x*y, not 2xy. You may enter sin, cos, tan, sqrt, exp, log, abs, pow, min, and max.
Why Curl Matters
Curl helps identify swirling motion. In fluid work, a large curl can show local spin. In physics, curl appears in Maxwell equations. In engineering, curl can help check rotational behavior near a chosen point. The result is a vector. Its three components show rotation around the x, y, and z axes.
Why Divergence Matters
Divergence is a scalar value. Positive divergence suggests a local source. Negative divergence suggests a local sink. A value near zero suggests balanced flow near the chosen point. This is useful when checking incompressible flow, field consistency, and conservation ideas.
Numerical Method
The calculator uses central differences. It evaluates each component slightly before and after the selected point. The selected step size controls this small movement. Smaller steps can improve accuracy for smooth fields. Very tiny steps may increase rounding error. A practical default is often enough for learning and quick checking.
Practical Tips
Use clean expressions and matching parentheses. Keep units consistent across all components. Try a larger step if the answer looks unstable. Compare simple fields with known answers first. Export the results when you need a record. The example table gives starter fields for testing. This calculator is a study and planning aid. It does not replace symbolic proof, laboratory calibration, or professional review.
Reading The Output
Look at divergence first when source strength matters. Then read the curl vector. A single large curl component means rotation is strongest around that axis. The curl magnitude gives compact rotation measure. Component values show the original field at the selected point. Derivative rows explain how the values were built.