What this calculator does
The lift coefficient, Cl, is a dimensionless number that captures how effectively a wing or airfoil shape converts airspeed and air density into lift, at a given angle of attack. It plays exactly the same role for lift that the drag coefficient plays for drag, but the two describe different forces acting on a body moving through air, and are measured and used separately.
The coefficient of lift formula is L = ½ρv²ACl, where L is lift force, ρ is air density, v is airspeed and A is wing area. Rearranged, Cl = 2L / (ρv²A). This calculator solves either direction: work out Cl from a measured or known lift force, or work out the lift force a given Cl would produce at a chosen speed and air density.
The formula
Dynamic pressure, ½ρv², is worked out first from air density and airspeed. Multiplying that by wing area and the lift coefficient gives lift force; dividing a known lift force by dynamic pressure and wing area gives the lift coefficient instead.
| Term | Meaning |
|---|---|
| Cl | Lift coefficient: a dimensionless number describing how much lift a given wing shape and angle of attack produce, relative to dynamic pressure and area. |
| L | Lift force, acting perpendicular to the airflow. |
| ρ | Air density; roughly 1.225 kg/m³ at sea level in standard conditions, falling with altitude. |
| ½ρv² | Dynamic pressure, the same quantity used in the drag equation. |
The inputs explained
| Field | What to enter |
|---|---|
| Solve for | Choose whether you are solving for the lift coefficient from a known force, or for the lift force from a known coefficient. |
| Lift force (L) (N) | The lift force being generated, used when solving for Cl. |
| Lift coefficient (Cl) | A known or assumed lift coefficient, used when solving for lift force. |
| Air density (sea level ≈ 1.225) (kg/m³) | Air density at the altitude and conditions in question; 1.225 kg/m³ is standard sea-level air. |
| Airspeed (m/s) | The airspeed relative to the surrounding air, not ground speed. |
| Wing area (m²) | The wing planform area used as the reference area. |
When to use it
Estimating a wing's lift coefficient from flight data
If a measured or calculated lift force is known at a given speed, this works backwards to the lift coefficient formula being achieved at that angle of attack, useful for comparing against published Cl curves for a given airfoil.
Sizing a wing for a target lift force
Given a target Cl (from an airfoil's known performance) and a required lift force at cruise speed, rearranging for wing area shows roughly how large a wing needs to be.
Comparing lift and drag on the same airframe
Lift and drag share the same dynamic-pressure term, so working out both coefficients for the same flight condition shows the lift-to-drag ratio, a key measure of aerodynamic efficiency.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the lift coefficient formula changes with airspeed at a fixed lift force
A fixed 1,200 N of lift and 16 m² of wing area, at a range of airspeeds.
| Airspeed | Lift coefficient (Cl) | Dynamic pressure |
|---|---|---|
| 20 m/s | 0.3061 | 245.00 Pa |
| 30 m/s | 0.1361 | 551.25 Pa |
| 40 m/s | 0.0765 | 980.00 Pa |
| 50 m/s | 0.0490 | 1,531.25 Pa |
| 60 m/s | 0.0340 | 2,205.00 Pa |
| 80 m/s | 0.0191 | 3,920.00 Pa |
How lift force changes with wing area at a fixed lift coefficient
A fixed lift coefficient of 0.5 at 40 m/s, across a range of wing areas.
| Wing area | Lift force | Dynamic pressure |
|---|---|---|
| 8 m² | 3,920.00 N | 980.00 Pa |
| 12 m² | 5,880.00 N | 980.00 Pa |
| 16 m² | 7,840.00 N | 980.00 Pa |
| 20 m² | 9,800.00 N | 980.00 Pa |
| 25 m² | 12,250.00 N | 980.00 Pa |
| 30 m² | 14,700.00 N | 980.00 Pa |
Questions
How is the lift coefficient formula different from the drag coefficient formula?
They have the same structure (a force equals dynamic pressure times area times a coefficient), but lift acts perpendicular to the airflow while drag acts along it. A wing has both a lift coefficient and a drag coefficient at any given angle of attack, and the two are calculated and plotted separately.
What is a typical value for the coefficient of lift?
It depends heavily on the airfoil shape and angle of attack, but many wings cruise around Cl of 0.3 to 0.6 and can reach a maximum Cl of around 1.5 to 2.0 near the stall angle, beyond which lift drops off sharply.
Why does Cl need a reference area?
Lift force depends on wing size as well as shape, so Cl is defined per unit of wing area (dynamic pressure times area) to isolate the effect of shape and angle of attack alone, letting wings of different sizes be compared on the same basis.
Does air density change the lift coefficient itself?
No. Cl is a property of the wing shape and angle of attack, not of air density. Density affects how much lift a given Cl produces at a given speed, but for the same shape and angle of attack, Cl itself stays essentially the same at different altitudes.
For the equivalent calculation on the drag side, see the drag coefficient calculator. To work directly with the dynamic-pressure term shared by both, see the drag force calculator.