Lift Coefficient Calculator

Background.

Raw lift figures are almost impossible to compare. Lift grows with the square of speed and in direct proportion to air density and wing area, so the numbers for a glider, an airliner and a wind-tunnel model have little in common. Divide the lift by the dynamic pressure, ½ρv², and by a reference area, and what remains is a pure number, the lift coefficient C_L, describing how hard the wing is working at that moment.

That number is what aerodynamicists plot against angle of attack, what airfoil catalogues tabulate, and what sets a stall speed. Every wing has a maximum C_L; ask for more and the airflow separates from the upper surface and lift collapses. Because lift depends on speed squared, flying at half the speed needs four times the lift coefficient to carry the same weight, which is why slow flight means a raised nose and lowered flaps.

Here the coefficient is recovered from the other four quantities: a lift force, the density of the air or water, the flow speed and the reference area. In steady level flight lift equals weight, so an aircraft's mass times 9.81 m/s² is a fair lift figure. Air in the standard sea-level atmosphere has a density of 1.225 kg/m³, and it thins with height and heat, to about 0.909 kg/m³ at 3,000 m.

A coefficient means something only alongside its reference area. Wings use planform area, while car aerodynamics usually quotes frontal area. The result also describes just the state you enter. It cannot predict lift from a wing's shape, angle of attack, Reynolds number or Mach number, and it makes no allowance for the extra lift a wing gains close to the ground.

What is lift coefficient calculator?

The lift coefficient C_L is a dimensionless number relating the lift on a body to the dynamic pressure of the flow and a chosen reference area: C_L = L ÷ (½ρv²A). For an aircraft wing the reference area is normally the wing's planform area, its outline seen from above. Because it has no units, the same C_L describes the same aerodynamic condition on a wind-tunnel model and a full-size aircraft, provided flow conditions such as Reynolds number and Mach number are comparable.

How to use this calculator.

1. 01Enter the lift force in newtons. For an aircraft in steady level flight use its weight, mass in kilograms times 9.81; a pound-force is 4.448 N.
2. 02Enter the fluid density: 1.225 kg/m³ for air in the standard sea-level atmosphere, less at altitude or on a hot day, and about 1,000 kg/m³ for fresh water if you are working on a hydrofoil.
3. 03Enter the flow speed in metres per second as true airspeed; one knot is 0.5144 m/s. Equivalent airspeed paired with the sea-level density of 1.225 gives the same answer, because both produce the same dynamic pressure.
4. 04Enter the reference area in square metres, using the same convention as any data you will compare with, usually the wing planform area. One square foot is 0.0929 m².

The formula.

C_L = 2L ÷ (ρv²A). The term ½ρv² is the dynamic pressure, the pressure the moving fluid would exert if brought to rest, in pascals. Multiplied by the reference area it becomes a force, and C_L is the ratio of the actual lift to that force; the 2 in the numerator comes from the one-half in the dynamic pressure. Speed enters squared, so it dominates the uncertainty: a speed 10% too high lowers C_L by about 17%, and 10% too low raises it by about 23%. The same error in lift, density or area moves the answer by roughly 10%. All four inputs must be positive, so a downforce has to be entered as a magnitude, and the coefficient reported is its size, without the negative sign often used for downforce.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NASA Glenn Research Center, Lift Equation.
2. [2]FAA, Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.