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Lift Equation Calculator

Enter the air density, velocity, wing area and lift coefficient.

Result

How it is calculated

Enter air density ρ in kg/m³, airspeed v in m/s, wing area A in m² and the lift coefficient CL (no unit). The tool first finds the dynamic pressure, then the lift:

q = ½ × ρ × v² (pascals)

L = q × A × CL (newtons)

It also expresses the lift in kilograms-force by dividing by 9.80665, so you can compare it directly with the aircraft's weight in kg. Results are shown with two decimals. Density and area must be above zero. Speed enters squared, so its sign does not matter, while a negative lift coefficient gives negative lift (a downward force). The equation assumes steady, level airflow and a coefficient that suits the wing's current angle of attack.

Worked example

A light aircraft wing of 16 m² flies at 30 m/s in sea-level air of density 1.225 kg/m³ with CL = 1.2.

  1. Dynamic pressure: 0.5 × 1.225 × 30² = 0.5 × 1.225 × 900 = 551.25 Pa.
  2. Lift: 551.25 × 16 × 1.2 = 10,584.00 N.
  3. In kilograms-force: 10,584 ÷ 9.80665 = 1,079.27 kgf.

That is enough to support a mass of about 1,079 kg in level flight, before any margin.

Try this example →

Common mistakes

  • Entering speed in km/h or knots. The field is metres per second, and 108 km/h is 30 m/s; typing 108 gives a lift 13 times too large because speed is squared.
  • Using sea-level density at altitude. Density falls with height, and lift falls in proportion, so a high airfield needs the local value of ρ rather than 1.225.
  • Applying a single lift coefficient to every speed and angle of attack. CL changes with angle of attack and flap setting, so use the value that matches the condition you are analysing.
  • Using the total aircraft area instead of the wing planform area. A is the reference wing area, usually quoted in the aircraft's data.
  • Comparing newtons with a weight in kilograms. 10,584 N is about 1,079 kgf; compare lift in N with weight in N (mass × 9.81), or use the kgf line with mass in kg.

Sources

About this calculator

The lift equation, L = ½·ρ·v²·A·Cl, is the core relation of fixed-wing aerodynamics: lift force L depends on air density ρ, the square of airspeed v, wing planform area A, and the lift coefficient Cl, which bundles together the airfoil shape and angle of attack. Because lift scales with the square of velocity, doubling airspeed quadruples the available lift, which is why aircraft need far less angle of attack — and much shorter runways — at high speed than at low speed.

Aircraft designers and pilots use this relation to size wings for a target stall speed, to compute takeoff and landing performance, and to understand why lift falls off sharply in thin, low-density air at high altitude. It has the same structure as the drag equation, D = ½·ρ·v²·A·Cd, with the coefficient swapped for the drag counterpart.

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Comments (1)

  • Editorial team

    You can use the tool backwards to estimate a stall speed. Put in the maximum lift coefficient for your wing, then change the speed until the kgf line matches the aircraft's mass; that speed is where the wing can only just hold the weight at that density. It is an estimate, as real wings and flap settings vary. What are you working on: a model, a drone, a light aircraft?

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