Drag Force & Terminal Velocity Calculator
Work out how fast something falls through air and how hard air pushes back. Solve the drag equation F = ½ρv²CdA and terminal velocity, see how long a fall takes to reach it, and the power a car needs to push through the air.
How to Use
- Pick Terminal velocity for a falling object, or Drag force for something moving through air at a known speed.
- Choose what to solve for. Terminal velocity can also give the mass, the frontal area or the drag coefficient; drag force can also give the speed.
- Enter the mass, the drag coefficient Cd and the frontal area A. For a ball, A = π × d² ÷ 4.
- Leave the air density at 1.225 kg/m³ (sea level, 15 °C) or enter your own, for example a lower value at altitude.
- Read the answer in the first readout and the graph of speed against time, or press a preset: skydivers, a raindrop, a baseball, a table-tennis ball or a car at 100 km/h.
Worked Example
A skydiver. 80 kg, lying flat with a typical Cd of 1.0 and 0.45 m² facing the air, at sea-level density 1.225 kg/m³. Drag equals weight when ½ × 1.225 × v² × 1.0 × 0.45 = 80 × 9.80665, so vt = √(1,569.06 ÷ 0.5513) = 53.35 m/s (192.1 km/h, 119.3 mph). Speed follows v = 53.35 × tanh(9.80665 t ÷ 53.35), reaching 95% after 9.965 s and 337.8 m.
A car at 100 km/h. Cd = 0.30 and A = 2.2 m² are typical for a modern hatchback. F = 0.5 × 1.225 × 27.78² × 0.30 × 2.2 = 311.9 N, and the power to push through the air is F × v = 311.9 × 27.78 = 8.664 kW, before rolling resistance.
The common mistake: dropping the ½. Writing drag as ρv²CdA and solving mg = ρv²CdA gives the skydiver vt = √(784.5 ÷ 0.5513) = 37.73 m/s, when the drag equation carries a factor of one half and the answer is 53.35 m/s. The ½ comes from the dynamic pressure ½ρv², the same term as in Bernoulli’s equation.
Show Work
Formulas
Typical drag coefficients from the classic shape charts (after Hoerner, Fluid-Dynamic Drag): sphere 0.47, cube face-on 1.05, long cylinder side-on 0.82, streamlined body 0.04. Modern cars are typically 0.25 to 0.35. The real value depends on speed, surface and how the object is oriented, so the presets use typical figures, not measurements.
From Newton’s Resistance to Supersonic Free Fall
Isaac Newton gave the first theory of air resistance in Book II of the Principia (1687), arguing that a body moving through a fluid is resisted in proportion to the density of the fluid, its cross-section and the square of its speed: the same ingredients as the modern drag equation. Galileo had already noticed that air, not weight, is why a feather falls slower than a stone.
Square-law drag is a fast-flow result. For very small or very slow objects, such as mist droplets or dust, George Gabriel Stokes showed in 1851 that drag is instead proportional to the speed itself, F = 6πμrv, which is why fog hangs in the air. The drag coefficient Cd was introduced to fold all the details of shape and flow into one measured number.
Terminal velocity also depends on the air. High up the air is so thin that drag is tiny: in 2012 Felix Baumgartner jumped from about 39 km and broke the speed of sound in free fall, then slowed as he fell into denser air. This calculator uses one density for the whole fall, which suits jumps and drops in the lower atmosphere.
About This Tool
This calculator solves the drag equation and the terminal-velocity balance for whichever value you need: the falling speed, the mass, the frontal area (handy for sizing a parachute) or the drag coefficient, and the drag force, speed or area for something moving at a steady speed. It uses the exact tanh solution for a fall from rest, so the time and distance to 95% of terminal velocity are calculated rather than guessed, and it draws the speed curve next to a no-air fall. Drag power shows why fuel use climbs so fast with speed.
Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Force Calculator, Projectile Motion Calculator, and Bernoulli & Fluid Pressure Calculator.
Frequently Asked Questions
What is terminal velocity?
It is the speed at which air drag on a falling object equals its weight, so it stops speeding up: vt = √(2mg ÷ (ρCdA)). An 80 kg skydiver lying flat, with a typical Cd of 1.0 and 0.45 m² of frontal area, falls at √(2 × 80 × 9.80665 ÷ (1.225 × 1.0 × 0.45)) = 53.35 m/s, or 192.1 km/h.
How long does it take to reach terminal velocity?
In theory forever, because the speed approaches it more and more slowly, so the useful figure is the time to 95%. From the exact solution v = vt tanh(gt ÷ vt), the skydiver gets to 95% after 9.965 s and 337.8 m of fall; a 2 mm raindrop gets there after only 1.259 s and 5.391 m.
What is the drag force formula?
F = ½ρv²CdA: half the air density times the speed squared times the drag coefficient times the frontal area. A car with Cd = 0.30 and A = 2.2 m² at 100 km/h (27.78 m/s) meets 0.5 × 1.225 × 27.78² × 0.30 × 2.2 = 311.9 N of drag, which takes 8.664 kW to overcome.
Why does driving faster use so much more fuel?
Drag rises with the square of speed and the power to beat it with the cube. The same car at 130 km/h meets 527.1 N of drag and needs 19.04 kW for it, 2.197 times the power at 100 km/h for a 30% rise in speed.
Do heavier objects fall faster in air?
Yes, when they are the same size and shape, because terminal velocity grows with √(m ÷ CdA). A 2.7 g table-tennis ball (40 mm) tops out at about 8.554 m/s, while a 145 g baseball (74 mm) reaches about 39.27 m/s with the typical drag coefficients used here. In a vacuum both would fall together.
How do I use the Drag Force & Terminal Velocity Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Skydiving
Belly-to-earth (CdA ≈ 0.45 m²) an 80 kg jumper falls at 192.1 km/h; head-down (about 0.21 m²) it is 281.2 km/h.
Parachute sizing
To land 90 kg at 5 m/s with an assumed Cd of 1.5, solve for the area: 38.43 m² of canopy.
Cars and fuel use
A Cd 0.30, 2.2 m² car needs 8.664 kW to push through the air at 100 km/h and 14.97 kW at 120 km/h.
Sports balls
A baseball dropped from a great height tops out near 39.27 m/s (87.85 mph), which is why balls dropped from towers can be caught.
Weather and raindrops
A 2 mm raindrop (4.189 mg) treated as a sphere with Cd 0.47 falls at about 6.739 m/s, reached within 5.391 m.
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