Curl Calculator
Work out curl instantly with clear inputs, formula shown and shareable results.
About Curl Calculator
The curl measures local rotation, with components (∂Fz/∂y − ∂Fy/∂z, ∂Fx/∂z − ∂Fz/∂x, ∂Fy/∂x − ∂Fx/∂y). A zero curl means the field is conservative and derives from a scalar potential.
Formula
Curl
∇ × F = (∂Fz/∂y − ∂Fy/∂z, ∂Fx/∂z − ∂Fz/∂x, ∂Fy/∂x − ∂Fx/∂y)
Worked example
With the default values below, Curl Calculator returns Curl ∇ × F of (3, -3, 4). Change any input above and every figure here is recalculated in your browser.
Inputs used
- ∂Fz/∂y and ∂Fy/∂z as a pair
- 5, 2
- ∂Fx/∂z and ∂Fz/∂x as a pair
- 1, 4
- ∂Fy/∂x and ∂Fx/∂y as a pair
- 7, 3
Results
- Curl ∇ × F
- (3, -3, 4)
- Magnitude of the curl
- 5.83095189
- Interpretation
- Non-zero curl — the field rotates about the reported axis
- z component
- 4.000000
Step by step
- 1Values used
- 2Curl
- 3Curl ∇ × F= (3, -3, 4)
- 4Magnitude of the curl= 5.83095189
- 5Interpretation= Non-zero curl — the field rotates about the reported axis
- 6z component= 4.000000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
For the sample pairs?
The curl is (3, −3, 4), of magnitude √34 ≈ 5.8309519.
Why does zero curl matter?
It means line integrals depend only on the endpoints, so the field is conservative and work around any closed loop is zero.