Drag Force Calculator: F = 1/2 rho v^2 Cd A

The drag on an object moving through air or water.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • F_D = \tfrac12\rho v^2C_DA
  • v = \sqrt{\frac{2F_D}{\rho C_DA}}
  • C_D = \frac{2F_D}{\rho v^2A}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the drag force: drag force = 1/2 x density of the fluid x speed^2 x drag coefficient x frontal area
  2. Put the values in (every value in its SI unit): drag force = 1/2 x 1.225 x 30^2 x 0.3 x 2.2
  3. The answer: drag force: 363.825 N
  4. The same answer in other units: 0.363825 kN; 37.0998 kgf; 81.7911 lbf

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Speed; Drag force (leave it as it is if this is what you are finding) 363.825 N; Drag coefficient (leave it as it is if this is what you are finding) 0.3; Frontal area (leave it as it is if this is what you are finding) 2.2 m2.

  1. The formula, arranged to find the speed: speed = square root of ((drag force) / (1/2 x density of the fluid x drag coefficient x frontal area))
  2. Put the values in (every value in its SI unit): speed = square root of ((363.825) / (1/2 x 1.225 x 0.3 x 2.2))
  3. The answer: speed: 30 m/s
  4. The same answer in other units: 108 km/h; 67.1081 mph

Common questions

What is the drag equation?

Drag equals half the fluid density times the speed squared times the drag coefficient times the frontal area.

What is a drag coefficient?

A number that sums up how streamlined the shape is. The lower it is, the less drag the shape has for its size.

How does drag change with speed?

With the square of the speed. At twice the speed the drag is four times as big.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics or physics text (drag force).

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