Lift Force Calculator (Lift Equation L = ½ρv²SC_L)
By Santaji GadepatilinUpdated November 2, 2026
The lift equation relates the upward force on a wing to air density, the square of airspeed, wing area and a lift coefficient that captures the wing's shape and angle of attack. This lift force calculator gives the lift in newtons and the mass it can support, and can solve backwards for the take-off speed or wing area you need.
How to use the lift force calculator
Enter the air density, the airspeed, the wing (reference) area and the lift coefficient. The calculator returns the lift force and the mass that lift can hold up against gravity. To find the speed needed to fly, enter the mass and clear the airspeed. The same equation works for hydrofoils — use water’s density.
Lift equation
L = ½ ρ v² S CL · m = L ÷ g
Example
A light aircraft with 16 m² of wing flies at 50 m/s (97 knots) in sea-level air with CL = 0.5:
- L = 0.5 × 1.225 × 50² × 16 × 0.5 = 12,250 N
- Mass supported = 12,250 ÷ 9.80665 = 1,249 kg
Air density and lift with altitude (ISA)
Same wing, speed and CL as the example; the last column is the true airspeed that restores sea-level lift.
| Altitude | Density | % of sea level | Lift at 50 m/s | Speed for equal lift |
|---|---|---|---|---|
| 0 m | 1.2250 kg/m³ | 100.0% | 12.25 kN | 50.0 m/s |
| 1,000 m | 1.1116 kg/m³ | 90.7% | 11.12 kN | 52.5 m/s |
| 2,000 m | 1.0065 kg/m³ | 82.2% | 10.06 kN | 55.2 m/s |
| 3,000 m | 0.9091 kg/m³ | 74.2% | 9.09 kN | 58.0 m/s |
| 4,000 m | 0.8191 kg/m³ | 66.9% | 8.19 kN | 61.1 m/s |
| 5,000 m | 0.7361 kg/m³ | 60.1% | 7.36 kN | 64.5 m/s |
| 6,000 m | 0.6597 kg/m³ | 53.9% | 6.60 kN | 68.1 m/s |
| 8,000 m | 0.5252 kg/m³ | 42.9% | 5.25 kN | 76.4 m/s |
| 10,000 m | 0.4127 kg/m³ | 33.7% | 4.13 kN | 86.1 m/s |
Densities follow the International Standard Atmosphere troposphere model; hot days reduce density further.
Notes
- CL rises roughly linearly with angle of attack (about 0.1 per degree for a typical wing) until the stall.
- Lift always comes with induced drag; estimate the parasitic part with the drag force calculator.
- Use true airspeed, not indicated airspeed, with the actual air density.
Frequently asked questions
What is the lift equation?
L = ½ ρ v² S C_L, where ρ is air density, v the true airspeed, S the wing area and C_L the lift coefficient. Doubling the speed quadruples the lift.
What is a typical lift coefficient?
Cruise values are about 0.3–0.6. A clean wing reaches a maximum of roughly 1.2–1.6 just before stalling, and flaps raise C_L,max to about 2–3.
How do I find the take-off or stall speed?
Set the lift equal to the weight and solve v = √(2mg ÷ (ρ S C_L,max)). Enter the mass, clear the airspeed field and the calculator solves for it.
Why do aircraft need longer runways at high altitude?
Thinner air means less lift at the same speed, so the aircraft must reach a higher true airspeed — about 16% higher at 3,000 m — before it can lift off.