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Divergence & Curl Calculator

Compute divergence and curl of a 3D field at a point.

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div F = P_x+Q_y+R_z ， curl F = (R_y−Q_z, P_z−R_x, Q_x−P_y)
e.g. x^2
e.g. y*z
e.g. z

📖 Tutorial | Divergence & Curl

1. Definition
Divergence div F=P_x+Q_y+R_z is a scalar source strength. Curl curl F=(R_y−Q_z,P_z−R_x,Q_x−P_y) is a vector rotation.
2. Symbols
(P,Q,R)vector field
divdivergence (scalar)
curlcurl (vector)
3. How it works
  • Numerically differentiate;
  • Combine into div and curl.
4. Steps
  1. Enter P, Q, R and point;
  2. Click Calculate.
5. Example
Example: F=(x²,yz,z) at (1,2,3).
Solution: div=2+3+1=6; curl=(y,0,0)=(2,0,0).
6. Pitfalls
div is scalar, curl is vector;
Positive div is a source;
Zero curl is irrotational.

❓ FAQ | Divergence & Curl

Meaning of divergence?
Outflow per unit volume.
Curl direction?
Rotation axis by right-hand rule.
Irrotational?
curl F=0, e.g. electrostatic.
Sourceless?
div F=0.
2D curl?
Q_x−P_y in Green's theorem.