Lift force calculator
Enter the lift coefficient, the wing area, the air density and the airspeed to get the lift force. Switch the unknown to find how fast a wing must fly to carry a weight, or which lift coefficient it needs at a given speed. Sea-level standard air, 1.225 kg/m³, is the default.
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How to use it
- Choose what to find: lift, airspeed or lift coefficient.
- Enter the wing area, the air density and the other known values.
- Read the result; “mass it can hold up” is the lift divided by g, the load in kilograms the wing supports in level flight.
- Lift: L = ½ ρ v² S C_L.
- Airspeed: v = √(2L ÷ (ρ S C_L)).
- Lift coefficient: C_L = 2L ÷ (ρ v² S).
- Dynamic pressure: q = ½ ρ v²; wing loading = L ÷ S.
Worked example
A light aircraft wing of 16.2 m² at C_L = 1.0 and 30 m/s in sea-level air: L = 0.5 × 1.225 × 30² × 16.2 × 1.0 = 8,930.25 N, enough to hold up 910.63 kg. The dynamic pressure is 551.25 Pa.
What speed does the same wing need to carry 10,000 N at C_L = 1.2? v = √(2 × 10,000 ÷ (1.225 × 16.2 × 1.2)) = √839.84 = 28.98 m/s.
Tips
- Wing area. It is the planform seen from above, including the part of the wing that passes through the fuselage, as usually quoted.
- Level flight means lift = weight. Enter the aircraft’s weight as lift to get the speed at a given C_L.
- The equation is not the whole story. It assumes a known C_L; finding that C_L for a new shape takes wind tunnel or CFD data.
Frequently asked questions
What is the lift equation?
Lift L = ½ × ρ × v² × S × C_L, where ρ is the air density, v the airspeed, S the wing area and C_L the lift coefficient. The term ½ρv² is the dynamic pressure, so lift is dynamic pressure times area times a shape-and-angle factor.
What lift coefficient should I use?
C_L depends on the airfoil and the angle of attack. Typical wings cruise at about 0.2 to 0.5 and reach a maximum of roughly 1.2 to 1.8 just before the stall, higher with flaps. For a real design, take C_L from the airfoil's polar data.
Why does speed matter so much?
Lift grows with the square of speed. Fly 10 % faster and lift rises about 21 %; halve the speed and lift drops to a quarter. That is why the stall speed is found by solving the equation for v with the maximum C_L.
What air density should I enter?
1.225 kg/m³ is the standard atmosphere at sea level and 15 °C. Density falls with altitude and heat, about 1.007 kg/m³ at 2,000 m in the standard atmosphere, so a wing needs more speed for the same lift there. The density altitude calculator helps with real conditions.