Calculate related rates, from dy/dx and dy/dt to ladder, circle, and sphere problems for area, volume, and changing dimensions easily.

Related Rate Calculator

Ratio (dy/dx)
Chain Rule (dy/dt)
Common Problems

Enter exactly two values to calculate the missing one.

Related Rate Formula

The following two example problems outline the steps and information needed to calculate a rate of change such as dy/dx.

(dy) / (dx) = (ฮ” y) / (ฮ” x) (dy) / (dt) = (dy) / (dx) ร— (dx) / (dt)
  • Where ฮ”x is the change in x and ฮ”y is the change in y.
  • dy/dx is the rate of change of y with respect to x (slope).
  • If x and y both depend on time t, then dy/dt can be found using the chain rule dy/dt = (dy/dx)(dx/dt).

To estimate dy/dx from finite changes, divide ฮ”y by ฮ”x. For classic calculus โ€œrelated ratesโ€ problems (ladder, circle, sphere, etc.), you typically differentiate a relationship with respect to time to connect dy/dt and dx/dt.

How to Calculate Related Rate?

The following example problems outline how to calculate a related rate.

Example Problem #1:

  1. First, determine the change in y (ฮ”y).
    • The change in y is given as: 40.
  2. Next, determine the change in x (ฮ”x).
    • The change in x is provided as: 80.
  3. Finally, calculate the rate dy/dx using the equation above. 

dy/dx = ฮ”y / ฮ”x

The values provided above are inserted into the equation below and computed.

dy/dx = 40 / 80 = 0.50

Example Problem #2: 

For this problem, the variables required are provided below:

change in y (ฮ”y) = 60

change in x (ฮ”x) = 80

Test your knowledge using the equation and check your answer with the calculator.

dy/dx = ฮ”y / ฮ”x = ?