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Drag Equation Calculator

Work out the drag force, how hard air or water pushes back on a moving object, from density, speed, shape and area. Or solve for any of them.

Level: Grades 11–12

Printable worksheet

Drag Equation Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for

Air at sea level and 15 °C is about 1.225 kg/m³; fresh water is about 1,000 kg/m³.

A number with no units that sums up how streamlined the shape is. Roughly 0.25–0.35 for a modern car, about 0.47 for a sphere, about 1.0–1.3 for an upright cyclist or flat plate.

Result

Drag force

363.825 N

Drag force is 363.825 N.

In kilonewtons
0.3638 kN
In pounds-force
81.7911 lbf
Dynamic pressure (½ρv²)
551.25 Pa
Power to overcome drag
10,914.75 W
Power in kilowatts
10.9148 kW

See the step-by-step solution ↓

Step-by-step solution

  1. Multiply half the density (ρ) by the speed squared (v²), the shape number (Cd) and the area (A). That gives the drag force F

    0.5×1.225×302×0.3×2.2=363.825 N

  2. Multiply the force by the speed to get the power (P) spent fighting drag each second, in watts

    363.825×30=10,914.75 W

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how hard air or water pushes back on something moving through it. Anything moving through air or water has to push that fluid out of its way, and the fluid pushes back. That push is called drag. For most everyday objects at everyday speeds, it follows the drag equation: F = ½ × ρ × v² × Cd × A. F is the drag force. ρ (the Greek letter rho) is the fluid's density, or how heavy it is for its size. v is the speed through the fluid, and A is the front area facing the flow. Cd is the drag coefficient, a number that sums up how streamlined the shape is.

The squared speed is the surprising part. Going twice as fast means four times the drag force. Power is force times speed, so it also takes eight times the power just to hold that speed. This calculator finds the drag force. It can also work backward to the speed, Cd or area that would give a force you know. It always shows the dynamic pressure and the power spent fighting drag.

Where it's used

Why this math matters outside the classroom:

  • Cycling. Cyclists tuck low to shrink their frontal area and drag coefficient, which cuts drag at the same speed.
  • Highway speed. Engineers know drag grows with the square of speed, so 120 km/h brings about 1.44 times the drag of 100 km/h.
  • Parachutes. Parachute designers size the canopy so drag balances a jumper's weight at a safe landing speed.
  • Car drag. A car with Cd 0.3 and 2.2 m² frontal area at 30 m/s in air of 1.2 kg/m³ meets ½ × 1.2 × 900 × 0.3 × 2.2 ≈ 356 N of drag.

Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what to solve for: the drag force, the speed, the shape number (Cd) or the area.
  2. Enter the fluid density. The default is air at sea level.
  3. Fill in the other values you know, with their units.
  4. Read the answer, along with the dynamic pressure and the power needed to overcome drag.

What the inputs mean

Fluid density (ρ)
Air at sea level and 15 °C is about 1.225 kg/m³. It gets thinner with altitude and heat (around 1.0 kg/m³ at 2,000 m). Fresh water is about 1,000 kg/m³ and seawater about 1,025 kg/m³.
Speed relative to the fluid (v)
The object's speed relative to the fluid. A headwind adds to your ground speed; a tailwind subtracts from it.
Drag coefficient (Cd)
Cd has no units. It depends on shape and, to a lesser degree, on speed. Published values are usually measured in wind tunnels, for a stated reference area.
Reference (frontal) area (A)
Use the same reference area that Cd was measured with. That's usually the front area you see head-on.

Formula and method

F = ½ × ρ × v² × Cd × A
v = √(2F ÷ (ρ × Cd × A))
Cd = 2F ÷ (ρ × v² × A)
A = 2F ÷ (ρ × v² × Cd)
P = F × v

F is the drag force, ρ is the fluid density, v is the speed, A is the area and Cd is the drag coefficient. P is the power, the energy spent each second. The other lines are the same equation rearranged to solve for v, Cd or A.

The group ½ρv² is called the dynamic pressure. It's the pressure the fluid would press with if it were brought to a stop against the object. Multiplying it by the area gives a force. Then Cd scales that force to match the real shape. A flat plate sits near 1.2, a sphere near 0.47 and a smooth teardrop below 0.1.

The calculator first changes all inputs to metric (SI) units: kg/m³, m/s and m². That way the force comes out in newtons. The power figure is how fast work is done against drag at a steady speed, in watts.

Worked example

A car with a drag coefficient of 0.3 and a frontal area of 2.2 m² drives at 30 m/s (108 km/h) through sea-level air at 1.225 kg/m³. How much drag does it face?

  1. F = 0.5 × 1.225 × 30² × 0.3 × 2.2 = 363.825 N.
  2. Dynamic pressure: ½ × 1.225 × 30² = 551.25 Pa.
  3. Power to overcome drag: 363.825 × 30 = 10,914.75 W.

Result: The car faces about 364 N of drag (roughly 81.8 lbf, or pounds of force). It spends about 10.9 kW just pushing through the air at that speed.

Understanding the result

At highway speeds, drag is usually the biggest single load on a car. That's why fuel use rises sharply above about 90 km/h. Cutting speed by 10% cuts the drag force by about 19% and the power by about 27%.

For cyclists and runners, Cd × A (often called the drag area) matters more than either one alone. Tucking down shrinks the area, and often Cd too.

Assumptions and limitations

  • Cd is treated as fixed at the speed given.
  • The fluid is steady and the same density throughout; the speed is relative to that fluid.
  • Speeds are well below the speed of sound, so the air's squeezing (compressibility) can be ignored.
  • Cd changes with the Reynolds number, a measure of how smooth or swirly the flow is. So a value measured at one speed or size may not hold at very different speeds or sizes.
  • Near or above the speed of sound, shock waves add wave drag that this equation doesn't capture.
  • For very small or very slow objects, such as dust in air, drag grows with the speed itself rather than its square. Stokes' law applies instead.

Frequently asked questions

What is a typical drag coefficient?

Very roughly, a smooth teardrop is around 0.05–0.1 and a modern car 0.25–0.35. A sphere is about 0.47, an upright cyclist around 0.9, and a flat plate facing the flow about 1.2. Always pair the value with the area it was measured against.

Why does drag depend on the square of the speed?

At higher speed, the object pushes more fluid out of the way each second. It also gives each bit of fluid a bigger shove. Both effects grow in step with the speed, so together they grow with its square.

Is drag the same as air resistance?

Air resistance is drag in air. The same equation works in water or any other fluid; you just use that fluid's density. That's why swimming feels so much harder than running at the same speed.

How does drag relate to terminal velocity?

A falling object speeds up until the drag force equals its weight. That top speed is its terminal velocity. Set m × g (mass times gravity, which is the weight) equal to ½ρv²CdA and solve for v. You can do that here: enter the weight in newtons as the force and solve for speed.

How this calculator is checked

Method: Standard quadratic drag equation of fluid dynamics, F = ½ρv²CdA, with power P = Fv. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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