🛩️ The Lift Equation

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

How airspeed, wing area, and airfoil shape combine to produce the force that holds an aircraft up.

A wing generates lift by deflecting airflow and creating a pressure difference between its upper and lower surfaces — the lift equation doesn't model that flow physics directly, but instead packages the whole complicated result into one coefficient (Cl) that's been measured or computed for a given airfoil shape and angle of attack, then combines it with the more straightforward physical quantities: how dense the air is, how fast the aircraft moves through it, and how much wing area is doing the work.

Lift scales with the square of airspeed, which is the single most important practical consequence of this equation — flying twice as fast produces four times the lift at the same coefficient and air density, which is why aircraft need much less angle of attack (and correspondingly lower Cl) to maintain level flight at high speed than at low speed.

Air density itself drops with altitude, which is why lift equation problems are commonly worked at a specific reference altitude using standard-atmosphere density values — the same wing at the same airspeed produces less lift at 35,000 feet than at sea level, simply because there's less air to deflect.

Key formula

L = 0.5 × ρ × v² × A × Cl

Variables

ρ

air density, which decreases with altitude

Cl

lift coefficient — captures the airfoil shape and angle of attack's effect on lift, usually determined experimentally or computationally

How to use the Lift Equation calculator

Use this to find how much lift a wing produces at a given airspeed, wing area and lift coefficient, at one of four standard-atmosphere altitudes. It is the equation behind stall speed, wing sizing for a model or a light aircraft, and the reason lift depends so strongly on speed.

The lift coefficient is what encodes the wing shape and how hard it is being worked: it rises with angle of attack until the wing stalls, and flaps raise the maximum. Enter the value that applies to your condition, and use the true airspeed for the altitude you select.

Altitude (ISA standard atmosphere)

The standard-atmosphere altitude, which sets the air density. Air at 10,000 ft is about three quarters as dense as at sea level, and at 35,000 ft less than a third.

Airspeed (knots)

The true airspeed of the wing through the air, in knots. If you have indicated airspeed instead, use the sea-level altitude, since indicated airspeed already reflects dynamic pressure.

Wing Area (ft²)

The planform area of the wing in square feet: span times average chord, measured including the part of the wing that passes through the fuselage.

Lift Coefficient (Cl)

The dimensionless lift coefficient. A typical wing at cruise angle of attack is around 0.3 to 0.6, and with flaps a light aircraft can reach about 1.5 to 2.0 just before stalling.

Worked example: a light aircraft on final approach

A light aircraft with a 174 ft² wing and a weight of 2,400 lb is on final approach at 65 knots at sea level, flaps extended, with a lift coefficient of 1.6. How much lift does the wing make, and how does that compare with the weight?

Worked by hand:

1. Speed in SI. 65 knots × 0.5144 = 33.4 m/s.
2. Dynamic pressure. ½ρV² = 0.5 × 1.225 × 33.4² = 685 Pa (sea-level density 1.225 kg/m³).
3. Wing area in SI. 174 ft² × 0.0929 = 16.17 m².
4. Lift. L = ½ρV² × S × C_L = 685 × 16.17 × 1.6 = about 17,700 N, which the calculator converts to 3,982 lb.
5. Compare with the weight. 3,982 ÷ 2,400 = 1.66.

At this speed and lift coefficient the wing could support about 1.66 times the aircraft's weight, so the aircraft is well clear of the stall. Setting lift equal to weight and solving for speed gives the stall speed at this lift coefficient, about 50.5 knots. Because lift depends on the square of speed, halving the speed cuts lift to a quarter, and at 35,000 ft, where the air is less than a third as dense, the same wing needs about 1.8 times the true airspeed to make the same lift.

Reading the result: what lift depends on

Lift is one half of the density times the speed squared times the wing area times the lift coefficient, and every factor has a lesson in it. Speed matters most, because it is squared. Density is why aircraft fly faster at altitude. Area is why heavy aircraft have big wings. The coefficient is the part a pilot controls with angle of attack and flaps.

• A wing stalls when its angle of attack passes a critical value, typically around 15 to 18 degrees, and the lift coefficient then drops. The maximum lift coefficient sets the stall speed: raise it with flaps and the stall speed falls.
• In a turn the wing must carry more than the aircraft's weight, so stall speed rises with the square root of the load factor. A 60-degree bank doubles the load and raises the stall speed by about 41 percent.
• Use indicated airspeed with sea-level density, or true airspeed with the actual density; mixing them gives the wrong answer.
• The lift coefficient here is for the whole wing. A published airfoil section coefficient is higher than a finite wing's, because the wingtips reduce lift.

Notes & limitations

• Cl isn't a fixed property of a wing — it varies with angle of attack, increasing (up to a point) as the wing pitches up, until it reaches a maximum and then drops sharply at the stall angle, where the smooth airflow the whole equation depends on breaks down.
• This is the same basic equation form used for the Drag Equation elsewhere on PhDino, just with a different coefficient (Cl vs. Cd) and a different physical effect being modeled — both forces come from the same airflow interacting with the same surface.

Common mistakes

• Mixing knots, miles per hour and metres per second. The calculator expects knots.
• Using density at the wrong altitude, or true airspeed together with sea-level density.
• Taking an airfoil's section lift coefficient as the coefficient of the whole wing.
• Forgetting the load factor. In a turn, a pull-up or turbulence the wing carries more than one times the weight, and the stall speed rises accordingly.
• Confusing lift with weight. In steady level flight they are equal, but the lift equation gives what the wing makes, not what is needed.

Frequently asked questions

Papers worth reading

Low-Reynolds-number airfoils Lissaman, P. B. S. (1983), Annual Review of Fluid Mechanics. Reviews how wing sections behave at low Reynolds numbers, where small aircraft and drones fly and the lift coefficient you assume matters most.