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Curl calculator

Compute the curl of a vector field: the scalar curl ∂Q/∂x − ∂P/∂y in 2D, or the full vector curl ∇×F = ⟨R_y − Q_z, P_z − R_x, Q_x − P_y⟩ in 3D. Enter each component in x, y, z and get every partial symbolically plus the curl evaluated at an optional point.

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Curl calculator is free to use as often as you like, directly from this page. It covers the scalar curl ∂Q/∂x − ∂P/∂y in 2D, or the full vector curl ∇×F = ⟨R_y − Q_z, P_z − R_x, Q_x − P_y⟩ in 3D. Enter each component in x, y, z and get every partial symbolically plus the curl evaluated at an optional point — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Curl calculator do?

Compute the curl of a vector field: the scalar curl ∂Q/∂x − ∂P/∂y in 2D, or the full vector curl ∇×F = ⟨R_y − Q_z, P_z − R_x, Q_x − P_y⟩ in 3D. Enter each component in x, y, z and get every partial symbolically plus the curl evaluated at an optional point.

What does a concrete case look like?

F = (−y, x, 0) → rot F = (0, 0, 2) — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in the scalar curl ∂Q/∂x − ∂P/∂y in 2D, or the full vector curl ∇×F = ⟨R_y − Q_z, P_z − R_x, Q_x − P_y⟩ in 3D. Enter each component in x, y, z and get every partial symbolically plus the curl evaluated at an optional point. Change any of them and the output follows immediately.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

What else is filed next to it?

Antilog Calculator (inverse logarithm), Average rate of change calculator and Bernoulli ODE Solver share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

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