⏱️Related Rates Calculator

Pick a classic scenario and get the unknown rate with the full implicit-differentiation derivation.

Ladder length L (ft)

Base distance from wall x (ft)

dx/dt — base sliding away (ft/s)

Free Related Rates Calculator

Related rates problems are notorious for being more about setup than calculus — our free related rates calculator handles both. Pick a classic scenario like a sliding ladder, an expanding balloon, or a draining cone, enter the known values and rates, and get the unknown rate instantly with the full derivation shown.

Each scenario starts from its governing geometric equation, which is then differentiated implicitly with respect to time, with every chain-rule term explained before the known values are substituted in and solved. Sign conventions (rates increasing vs. decreasing) are stated explicitly to avoid the most common source of related-rates mistakes.

Pick your scenario to get started. No sign-up, no downloads, no limits.