Terminal Velocity Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Dec 14, 2021

This terminal velocity calculator will help you estimate the speed of a free-falling object through a gaseous or liquid medium. The most common idea to connect this concept of terminal velocity is skydiving, i.e., humans falling through the air as a medium. This terminal velocity of say, a baseball would depend on factors like properties of object like mass, shape, and size as well as the density of the medium and gravitational acceleration.

So if you throw a penny in the air or fire a gun, what is the terminal velocity of the bullet or penny? Read on to understand the definition of terminal velocity and how to find terminal velocity.

What is terminal velocity?

As an object falls through the air, the velocity increases until a point where the gravitational pull is equal to the drag force on the object. At this point, the object's velocity is known as terminal velocity. Consider an object having mass, mm, the total force, FF acting on the object is:

F=mg12ρvt2ACd\quad F = mg - \frac{1}{2} \, \rho \, v_t^2 A C_d

where:

  • ggGravitational acceleration;
  • ρρDensity of fluid;
  • vvVelocity of object;
  • AACross-sectional area; and
  • CdC_dCoefficient of drag

Under the equilibrium conditions, the net force becomes zero and the velocity becomes terminal velocity. Upon rearranging the terms, the terminal velocity equation is:

vt=2mgρACd\quad v_t = \sqrt \frac{2 m g }{\rho A C_d}

Factors affecting terminal velocity and examples

There are two types of factors that affect the terminal velocity:

Let's first look at each object dependant factor:

  • Drag coefficient: This parameter depends on the object's shape. Such that a more streamlined body would have a lower drag compared to a blunt body.

  • Area: The larger the area of the object, the lower the terminal velocity of the object. For instance, the terminal velocity of a skydiver in a belly-to-earth direction will be lower than in the case where he pulls his limbs in.

  • Mass: A heavier object would have a higher terminal velocity than the lighter one. The terminal velocity of a penny would be less than that of a bullet.

Mass to area relation
Objects having a combination of lower mass and larger areas would have lower terminal velocity and vice versa. An example of this is the parachute.

And the two environmental dependant factors:

  • Density: As the density of the fluid medium reduces, the terminal velocity increases. These different mediums or density variations could also come from different planetary environments.

  • Acceleration due to gravity: This parameter is most applicable for different planets. The variation in gravitational acceleration is directly proportional to terminal velocity.

Acceleration of an object
When an object reaches terminal velocity, its acceleration reduces to 0, i.e., the object's speed becomes constant.

How to calculate terminal velocity

To calculate terminal velocity calculator:

  1. Select the shape of the object (this fills in the drag coefficient for that shape).
  2. Enter the mass of the object.
  3. Fill in the cross-sectional area.
  4. Insert the coefficient of drag (if you want to find the terminal velocity of a different shape).
  5. Enter the density of the fluid medium (default value is for air).
  6. Fill in the gravitational acceleration (default value is for Earth's gravity).
  7. The calculator will return the terminal velocity.

Drag coefficients
You can use the list of preset drag coefficients by picking the shape of the object.

Example: Using the terminal velocity calculator

What is the terminal velocity of a human skydiver having a mass of 75 kg and cross-sectional area 0.18 m²? Take drag coefficient as 0.7.

To calculate terminal velocity calculator:

  1. Enter the mass, m=75 kgm = 75 \text{ kg}.
  2. Fill in the cross-sectional area, A=0.18 m2A = 0.18 \text{ m}^2.
  3. Insert the coefficient of drag, Cd=0.7\text{C}_d = 0.7.
  4. The density of the fluid medium at 20 °C20\ °\text{C} is prefilled.
  5. The gravitational acceleration, g\text{g} is prefilled for you.
  6. Using terminal velocity formula:
  vt=2759.811.20410.180.7=98.48 m/s\scriptsize \quad \ \ v_t = \sqrt \frac{2 \cdot 75 \cdot 9.81 }{1.2041 \cdot 0.18 \cdot 0.7} = 98.48 \text{ m/s}

Units of terminal velocity
You can also adjust the units to find terminal velocity in mph. Have a go at answering the question, what is the terminal velocity of a penny? using our calculator.

FAQ

What do you mean by terminal velocity?

The steady speed at which an object free falls is known as the terminal velocity. As an object falls, its speed increases up to a point where the gravitational pull and drag force are equal. At this point, the velocity of the object becomes the terminal velocity, and the acceleration becomes zero.

What is the terminal velocity formula?

The equation that gives terminal velocity, v_t formula is:

v_t = √((2 × m × g)/(ρ × A × Cd))

where:

  • gGravitational acceleration in m/s2;
  • ρDensity of fluid in kg/m3;
  • ACross-sectional area in m2; and
  • CdCoefficient of drag.

How do I find terminal velocity?

To calculate terminal velocity:

  1. Multiply the mass of the object by the gravitational acceleration.
  2. Divide the resultant by the product of drag coefficient and projected area.
  3. Multiply the number in the previous step by 2.
  4. Divide the product by the density of fluid.
  5. Obtain the square root of the result to get the terminal velocity of the object.

What is terminal velocity of a baseball?

The terminal velocity of a baseball is 91.84 mph. Considering a circumference of 9.25 inches and 5.5 oz mass. The coefficient of drag for the baseball is taken as 0.3275. The terminal velocity is calculated by:

v_t = √((2 × 0.14883 × 9.81)/(1.2041 × 0.004393 × 0.3275)) = 40.7 m/s or 91.84 mph

What is terminal velocity of a golf ball?

The terminal velocity of a golf ball is 32.73 m/s. Considering a diameter of 2.1 cm and 1.25 oz mass. The coefficient of drag for the golf ball is taken as 0.389. The terminal velocity is calculated by:

v_t = √((2 × 0.03544 × 9.81)/(1.2041 × 0.001385442 × 0.389)) = 32.73 m/s

Rahul Dhari
Object
Shape
Select...
Mass (m)
lb
Cross-sectional area (A)
Coefficient of drag (Cd)
Environment
Density of fluid (ρ)
lb/cu ft
Acceleration due to gravity (g)
ft/s²
Velocity
Terminal velocity (Vₜ)
ft/s
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