About the Related Rates Calculator

Classic related-rates scenarios solved with full setup and derivation.

What it is

The Related Rates Calculator solves five classic related-rates scenarios โ€” a sliding ladder, an expanding sphere, a draining or filling cone, a growing shadow, and an expanding circle. For each, it states the governing geometric equation, differentiates it implicitly with respect to time, and substitutes your known values to find the unknown rate.

Features

Five scenarios

Sliding ladder, expanding sphere, draining cone, growing shadow, and expanding circle.

Full derivation

Governing equation, implicit differentiation, and substitution shown for every scenario.

Labelled diagrams

A simple diagram for each scenario matching the input variables.

Sign conventions

Explicit statement of whether each rate is increasing or decreasing.

Ready to use it?

Free, no sign-up required.

Open the Related Rates Calculator