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Curvature calculator

For a curve y = f(x), the curvature κ = |f″| / (1 + f′²)^(3/2) measures how sharply it bends at a point, and the radius of curvature is its reciprocal. Type a function and a point; the derivatives are taken symbolically, then evaluated.

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Curvature calculator is free to use as often as you like, directly from this page. It sits under Calculus in our catalogue, alongside Antilog Calculator (inverse logarithm) and Average rate of change calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Curvature calculator?

For a curve y = f(x), the curvature κ = |f″| / (1 + f′²)^(3/2) measures how sharply it bends at a point, and the radius of curvature is its reciprocal. Type a function and a point; the derivatives are taken symbolically, then evaluated.

What does a concrete case look like?

y = x², x = 0 → κ = 2, R = 0,5 — the tool shows every step in between, not just the final figure.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

What else is filed next to it?

Antilog Calculator (inverse logarithm), Average rate of change calculator and Bernoulli ODE Solver share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

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