Stokes Theorem Calculator
Work out stokes theorem instantly with clear inputs, formula shown and shareable results.
About Stokes Theorem Calculator
Stokes' theorem equates the circulation of a field around a closed curve with the flux of its curl through any surface bounded by that curve: ∮F·dr = ∬(∇×F)·n dA. Only the component of the curl along the normal contributes.
Formula
Stokes' theorem
∮C F · dr = ∬S (∇ × F) · n dA
Worked example
With the default values below, Stokes Theorem Calculator returns Circulation around the boundary of 17.32050808. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Curl component along the surface normal
- 2.5
- Surface areaminimum 0
- 8
- Angle between the curl and the normalaccepts 0–180 °
- 30 °
Results
- Circulation around the boundary
- 17.32050808
- Curl projected onto the normal
- 2.16506351
- Flux if the curl were fully aligned
- 20.00000000
- cos of the angle
- 0.86602540
Step by step
- 1Values used
- 2Stokes' theorem
- 3Circulation around the boundary= 17.32050808
- 4Curl projected onto the normal= 2.16506351
- 5Flux if the curl were fully aligned= 20.00000000
- 6cos of the angle= 0.86602540
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
With curl 2.5, area 8 and a 30° tilt?
The projected curl is 2.5 cos 30° ≈ 2.1650635, giving a circulation of about 17.3205081.
Does the surface choice matter?
No, as long as it is bounded by the same curve. That independence is exactly what the theorem asserts.