How this calculation works
Measure how sharply a regular plane curve turns at one point.
THE FORMULA
κ=|x′y″−y′x″|/(x′²+y′²)^(3/2)A worked example
A tangent velocity (1,0) and acceleration (0,2) give curvature 2.
Good to know
The velocity vector must be nonzero.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Measure how sharply a regular plane curve turns at one point.
The primary result is labeled “Curvature”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The velocity vector must be nonzero.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
A tangent velocity (1,0) and acceleration (0,2) give curvature 2.
Which rule does this calculator apply?
κ=|x′y″−y′x″|/(x′²+y′²)^(3/2)