Drag force: drag (F) is the aerodynamic resistance a fluid exerts on a moving object, given by F = ½ρv²CdA. This free calculator solves for the drag force or the speed — in any unit — and shows every step of the working.
Drag is the force a fluid — usually air or water — pushes back on something moving through it. To calculate it, use the drag equation: F = ½ · ρ · v² · Cd · A. Here ρ is the density of the fluid, v is the object’s speed relative to that fluid, Cd is the drag coefficient (a shape factor), and A is the frontal area facing the flow. The answer comes out in newtons (N) when every input is in SI units.
There are three steps. First, decide whether you want the drag force or the speed and select it in the calculator’s Solve for menu. Second, enter the fluid density — use the air or water preset, or type your own value — together with the speed, the drag coefficient and the frontal area; pick a shape preset such as Car or Sphere if you do not know Cd. The calculator converts km/h, mph and cm² to SI base units automatically. Third, read the answer alongside the worked steps, which show the formula, your numbers substituted in, and the final value with its units.
The squared speed term is the key to understanding drag. Because v is squared, drag rises far faster than speed: go twice as fast and you face four times the drag. The product Cd · A — often called the drag area — combines shape and size, so a small blunt object can drag as much as a large streamlined one. Keeping all four inputs consistent in SI units is what guarantees a correct result in newtons.
Drag governs how fast things can fall or coast. When an object falls, it accelerates until drag balances its weight, after which it descends at a steady terminal velocity — a relationship explored in depth in our guide to how terminal velocity works. To understand how a fluid’s density feeds into this equation, see the density calculator; for a definition of the term itself, see the physics glossary.
A car drives at 30 m/s (about 108 km/h) through air of density 1.225 kg/m³, with a drag coefficient of 0.3 and a frontal area of 2 m². Its drag force is F = ½ · 1.225 · 30² · 0.3 · 2 = 330.75 N. Now double the speed to 60 m/s: the drag jumps to F = ½ · 1.225 · 60² · 0.3 · 2 = 1323 N — four times as much, because the speed is squared. This is why fuel use climbs steeply at motorway speeds.
Drag determines fuel economy, top speed and range for cars, aircraft, cyclists and ships; it sets the terminal velocity of skydivers and raindrops; and it shapes the design of everything from wind turbines to spacecraft re-entry, where shedding kinetic energy as drag is the whole point.
The drag equation is F = ½ρv²Cd·A, where ρ is the fluid density, v is the speed relative to the fluid, Cd is the dimensionless drag coefficient that captures the object’s shape, and A is the frontal (reference) area facing the flow. The factor of one half comes from the dynamic pressure of the moving fluid.
Drag depends on the fluid’s dynamic pressure, which is ½ρv². Because the speed term is squared, doubling the speed gives four times the drag, and tripling it gives nine times. This is why air resistance grows so quickly on a fast car or a falling skydiver, and why high-speed travel is so energy-hungry.
The drag coefficient depends on shape. A smooth sphere is about 0.47, a modern car around 0.3, a cyclist near 0.9, a flat plate facing the flow about 1.28, and a belly-down skydiver close to 1.0. Streamlined shapes have lower coefficients; blunt shapes have higher ones.
The drag coefficient (Cd) describes how aerodynamic a shape is, while the frontal area (A) is how big it is when seen head-on. Drag depends on the product Cd·A, so a small but blunt object can have the same drag as a large but streamlined one. Engineers often quote CdA together as the “drag area”.
A falling object speeds up until the upward drag force equals its weight; at that point the net force is zero and it falls at a constant terminal velocity. Setting F = mg in the drag equation and solving for v gives the terminal velocity, which is why this calculator can also work backwards from a known drag force to find speed.