Related Rates Calculator
Author: Henrick YauRelated Rates Calculator - Available at: https://calculators.sg/related-rates-calculator/ - Accessed: 6 September 2026. Author: Henrick Yau.
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Calculate and analyse related rates problems in calculus. This calculator helps solve problems where two or more quantities change over time and are related by an equation, allowing you to find the rate of change of one variable with respect to time when given the rate of change of another variable.
Problem Type
Custom Equation Parameters
Cylinder Parameters
Cone Parameters
Sphere Parameters
Circle Parameters
Distance Between Points Parameters
Shadow Length Parameters
Rectangle Parameters
Triangle Parameters
Related Rates Solution
Solution Steps
Visualisation
Related Rates: Conceptual Overview
Understanding Related Rates
Related rates problems involve finding the rate of change of one quantity based on the knowledge of other changing quantities that are related by an equation. These problems are applications of implicit differentiation in calculus.
General Approach to Related Rates Problems
- Identify the known and unknown rates of change (derivatives with respect to time)
- Write an equation that relates the quantities whose rates are given or sought
- Implicitly differentiate the equation with respect to time
- Substitute the known values and rates
- Solve for the unknown rate
Common Related Rates Formulas
- Cylinder Volume: V = πr²h
- Cone Volume: V = (1/3)πr²h
- Sphere Volume: V = (4/3)πr³
- Circle Area: A = πr²
- Distance Between Points: d = √[(x₂-x₁)² + (y₂-y₁)²]
- Rectangle Area: A = lw
- Triangle Area: A = (1/2)bh
Key Concepts in Related Rates
- Implicit Differentiation: Taking the derivative of both sides of an equation with respect to time, treating all variables as functions of time
- Chain Rule: If y is a function of x and x is a function of t, then dy/dt = (dy/dx)(dx/dt)
- Rates of Change: Derivatives with respect to time (e.g., dr/dt, dV/dt)
- Instantaneous Rates: Related rates problems deal with rates at a specific moment in time
This calculator provides solutions for educational purposes. Always verify the results and understand the calculus concepts involved in related rates problems.