# What is the drag force?

Drag force calculator: F = ½CρAv² from the drag coefficient, fluid density, frontal area and speed, or the drag coefficient, area or speed from a known force, with the power to overcome drag.

- Page: https://www.acalculator.org/physics/drag-force-calculator
- JSON spec: https://www.acalculator.org/physics/drag-force-calculator.json
- Version: 7c12cab4aca7

## Default answer

Example with the default inputs (Find Drag force, Shape Skydiver, feet first, 0.70, Frontal area (A) 1.93750387500775 ft², Speed (v) 219.219756621331 mph, Fluid Air at sea level, 15 °C (1.225 kg/m³)): F = 741.189 N (166.626 lbf), with C = 0.7, ρ = 1.225 kg/m³, A = 0.18 m² and v = 98 m/s.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which value to work out from F = ½ × C × ρ × A × v². |
| F | Drag force (F) | The drag force on the object. |
| sh | Shape | The object, which sets its drag coefficient C (OpenStax Table 6.2). |
| C | Drag coefficient (C) | The drag coefficient of the object, a pure number. |
| A | Frontal area (A) | The area of the object that faces the flow. |
| v | Speed (v) | The speed of the object through the fluid (or of the fluid past it). |
| fl | Fluid | The air or water the object moves through, which sets the density ρ. |
| rho | Fluid density (ρ) | The density of the fluid. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The value worked out, to 6 significant figures. |
| force | Drag force (N) | F = ½ × C × ρ × A × v², in newtons. |
| lbf | Drag force (lbf) | The drag force in pounds-force. |
| cd | Drag coefficient C | The drag coefficient, a pure number. |
| area | Frontal area (m²) | The frontal area in square metres. |
| ft2 | Frontal area (ft²) | The frontal area in square feet. |
| speed | Speed (m/s) | The speed in metres per second. |
| mph | Speed (mph) | The speed in miles per hour. |
| kmh | Speed (km/h) | The speed in kilometres per hour. |
| q | Dynamic pressure (Pa) | ½ × ρ × v², in pascals: the drag force per unit of C × A. |
| power | Power to overcome drag (W) | P = F × v, in watts. |
| hp | Power to overcome drag (hp) | The same power in mechanical horsepower (745.7 W). |
| rho | Density used (kg/m³) | The fluid density in kilograms per cubic metre. |

## Method

F = ½ × C × ρ × A × v²; C = 2F ÷ (ρAv²); A = 2F ÷ (Cρv²); v = √(2F ÷ (CρA)); dynamic pressure q = ½ρv²; power P = F × v.

## Assumptions

- Drag grows with the square of the speed: large objects at moderate to high speed in air or water (OpenStax §6.4). Very small or slow objects follow Stokes’ law instead.
- C and A are for the same reference area (the frontal area); the fluid is still, and v is the relative speed.

## Worked examples

1. find = force, sh = skydiverFeet, A = 0.18, v = 98, fl = custom, rho = 1.21 gives F = 732.11292, lbf = 164.585532, result = F = 732.113 N (164.586 lbf), q = 5,810.42. Source: OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18).
2. find = speed, sh = skydiverFeet, A = 0.18, F = 735, fl = custom, rho = 1.21 gives v = 98.193041. Source: OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18).
3. find = cd, A = 0.7, v = 44, F = 819.896, fl = custom, rho = 1.21 gives C = 1, result = C = 1. Source: OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18), Example 6.17 (A = 0.70 m², C = 1.0, v_T = 44 m/s).
4. find = area, sh = sphere, v = 10, F = 2.75625, fl = air15 gives A = 0.1, power = 27.5625. Source: OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed (F_D = ½CρAv²; Table 6.2; skydiver: C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 75 kg, v_T = 98 m/s), https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed (retrieved 2026-10-18), Table 6.2 (sphere 0.45).

## FAQ

### How do you calculate drag force?

Multiply half the fluid density by the drag coefficient, the frontal area and the square of the speed: F = ½ × C × ρ × A × v². A skydiver falling feet first (C = 0.70, A = 0.18 m²) at 98 m/s through air of 1.21 kg/m³ feels ½ × 0.70 × 1.21 × 0.18 × 98² = 732 N.

### How do you calculate the drag coefficient?

Rearrange the drag equation: C = 2F ÷ (ρ × A × v²). With 819.9 N of drag on an area of 0.70 m² at 44 m/s in air of 1.21 kg/m³, C = 2 × 819.9 ÷ (1.21 × 0.70 × 44²) = 1.0.

### Why does drag grow with the square of the speed?

At the speeds of cars, cyclists and falling people, the force comes from pushing air out of the way. Twice the speed moves twice as much air each second, each with twice the speed, so the drag is 4 times larger.

### What are typical drag coefficients?

From OpenStax Table 6.2: an airfoil 0.05, a sphere 0.45, a skydiver feet first 0.70, a bicycle 0.90, a skydiver lying flat 1.0 and a circular flat plate 1.12. The cars in the table run from 0.28 to 0.37, a pickup truck is 0.43 and an SUV 0.64.

### How is drag force related to terminal velocity?

An object stops speeding up when drag equals its weight: mg = ½CρAv². Solving for v gives the terminal speed √(2mg ÷ (CρA)). Use Find: Speed with the weight as the force.

### How much power does it take to overcome drag?

Power is force times speed, P = F × v, so it grows with the cube of the speed. A sphere with 2.76 N of drag at 10 m/s needs 27.6 W.

## Sources

- OpenStax, University Physics Volume 1, §6.4 Drag Force and Terminal Speed: F_D = ½CρAv²; Table 6.2, typical drag coefficients; skydiver (75 kg, C = 0.70, A = 0.18 m², ρ = 1.21 kg/m³, 98 m/s); Example 6.17 (85 kg, A = 0.70 m², C = 1.0, 44 m/s), retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed
- OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure: Table 14.1 (air 1.29 kg/m³ at 0 °C and 101.3 kPa) and Table 14.2 (water 998.2 kg/m³ at 20 °C, sea water 1,030 kg/m³ at 0 °C), retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure
- U.S. Standard Atmosphere, 1976 (COESA; NOAA, NASA and USAF): sea-level density 1.225 kg/m³ at 288.15 K and 101,325 Pa, as given in the definition of the 1976 atmosphere by Public Domain Aeronautical Software, retrieved 2026-10-18. https://www.pdas.com/atmosdef.html (report: https://ntrs.nasa.gov/citations/19770009539)
- OpenStax, University Physics Volume 1, §7.4 Power: P = F × v, retrieved 2026-10-18. https://openstax.org/books/university-physics-volume-1/pages/7-4-power
- NIST Special Publication 811 (2008), Appendix B.8: 1 lbf = 4.4482216152605 N, 1 ft = 0.3048 m, 1 mph = 0.44704 m/s, 1 knot = 1,852 ÷ 3,600 m/s, 1 hp = 550 ft·lbf/s = 745.69987158227022 W, retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811