Contour Integral Calculator
Calculate complex contour integrals along closed curves in the complex plane.
Complex Function f(z) = u + iv
Express in terms of x = Re(z) and y = Im(z)
Contour (Circle)
Contour Integral
oint_C f(z) dz = oint_C (u + iv)(dx + i dy)
Contour Integral Result
-0.0000 + 0.0000i
|result| = 0.0000
ReReal Part
-0.000000
ImImaginary Part
0.000000
|z|Magnitude
0.000000
argArgument
99.35 deg
Contour Details
Center0 + 0i
Radius1
Contour Length6.2832
Key Theorems
- Cauchy's theorem: Analytic functions have zero integral
- Residue theorem: oint f dz = 2 pi i * sum(residues)
- For f(z) = 1/z around origin: oint dz = 2 pi i
About Contour Integrals
Definition
A contour integral integrates a complex function along a path in the complex plane. For analytic functions, the integral depends only on the endpoints (or is zero for closed paths).
Applications
- Evaluating real integrals
- Signal processing (Fourier/Laplace transforms)
- Quantum mechanics
- Fluid dynamics (conformal mapping)
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
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Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.