Coefficient of Lift Calculator
The lift coefficient relates the lift a wing produces to the dynamic pressure and the wing area. Solve for CL, lift L, dynamic pressure q or wing area S, with automatic unit conversion.
CL = L / ( q · S ) · q = ½ρV²
Inputs
Choose what to solve for, then fill in the other values. You can enter dynamic pressure q directly, or enter airspeed V and let the calculator compute q = ½ρV² from the air density.
Results
Enter values and press Calculate.
Lift diagram
Air flows over the wing section from the left with dynamic pressure q. The wing produces lift L perpendicular to the flow, spread over the planform area S seen from above. The lift coefficient CL is the lift as a fraction of q · S. The angle of attack in the sketch is only illustrative.
Reference tables
Common examples (illustrative values, computed by the same engine)
| Case | Lift L | q (Pa) | S (m²) | CL |
|---|
Typical lift coefficients (rough ranges, depend on the aircraft and wing section)
| Condition | Typical CL |
|---|---|
| Fast cruise | 0.2 – 0.4 |
| Economy cruise | 0.4 – 0.7 |
| Climb or slow flight, clean wing | 0.7 – 1.2 |
| Maximum for a clean wing, CL,max | 1.2 – 1.8 |
| Maximum with flaps or slats extended | 2.0 – 3.0 or more |
Standard air density (ISA)
| Altitude | Density ρ (kg/m³) | Density ρ (slug/ft³) |
|---|---|---|
| 0 m (sea level) | 1.225 | 0.002377 |
| 1000 m | 1.112 | 0.002156 |
| 3000 m | 0.909 | 0.001763 |
| 5000 m | 0.736 | 0.001429 |
| 8000 m | 0.526 | 0.001020 |
| 11 000 m | 0.364 | 0.000706 |
Key relations
| Quantity | Relation |
|---|---|
| Lift coefficient | CL = L / (q · S) |
| Lift | L = CL · q · S = ½ · ρ · V² · S · CL |
| Dynamic pressure | q = ½ · ρ · V² = L / (CL · S) |
| Wing area | S = L / (CL · q) |
| Airspeed from q | V = √( 2q / ρ ) |
| Level flight (L = W) stall speed | Vs = √( 2W / (ρ · S · CL,max) ) |
| Units | 1 lbf = 4.44822 N · 1 kgf = 9.80665 N · 1 psf = 47.8803 Pa · 1 ft² = 0.092903 m² |
Formula and notes
q = ½ · ρ · V²
- CL: lift coefficient (dimensionless)
- L: lift force, perpendicular to the oncoming flow
- q: dynamic pressure, ½ρV²
- S: reference wing area, normally the planform area
Example. A 1000 kg aircraft in level flight needs L = 1000 × 9.80665 = 9806.65 N. At 55 m/s in sea-level air (ρ = 1.225 kg/m³), q = ½ × 1.225 × 55² = 1852.8 Pa. With S = 16 m², CL = 9806.65 / (1852.8 × 16) = 0.331.
The lift coefficient is not a fixed property of a wing. It changes with angle of attack, flap setting, Reynolds number and Mach number, up to a maximum CL,max where the wing stalls. Always use the same reference area that the published coefficient uses. In steady level flight the lift equals the weight, so the calculator can be used with L = W.
Disclaimer. For education and estimation only. Do not use it for flight planning or aircraft design decisions without proper data and a qualified engineer.
References
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C_L | Lift coefficient | |
| L | Lift force | N |
| q | Dynamic pressure | Pa |
| S | Wing reference area | m2 |
What it means
The lift coefficient is the dimensionless factor that relates the lift generated by an airfoil or wing to the dynamic pressure and area. It depends on the angle of attack, airfoil shape, Reynolds number, and Mach number. C_L is obtained from experiments or CFD and is plotted in the lift curve (C_L vs α). The linear region (C_L = C_Lα · α) is used for small angles. The maximum C_L (C_Lmax) determines the stall speed. C_L is also used in performance calculations: cruise C_L is set for minimum drag, and high C_L for low‑speed flight. Understanding C_L is essential for designing wings that meet lift requirements at various flight conditions.
Worked example
Coefficient of Lift – Two Examples
Real‑World| Parameter | Value |
|---|---|
| L | 50,000 N |
| q | 3000 Pa |
| S | 20 m² |
| Parameter | Value |
|---|---|
| L | 15,000 N |
| q | 2000 Pa |
| S | 18 m² |
Common mistakes
- Coefficient of lift C_L: C_L = L / (q·S) – non‑dimensional.
- Lift L: In Newtons.
- Reference area S: Wing planform area (m²).
- C_L vs. angle of attack: C_L = C_Lα (α − α₀) for linear region; beyond stall, use experimental data.
- Units: All SI to get dimensionless C_L.
Applications
The coefficient of lift, C_L = L / (q·S), normalises the lift force by dynamic pressure and wing area, providing a dimensionless measure of lifting efficiency. It depends on angle of attack, airfoil shape, and Reynolds number. This coefficient is fundamental for plotting lift curves, determining stall angles, and designing high‑lift systems. Engineers use C_L to calculate the lift generated at a given flight condition, to compare aerodynamic performance of different wing designs, and to develop control laws. The maximum C_L (C_L,max) dictates stall speed. By using the lift coefficient, aerospace engineers can systematically analyse and optimise the lifting performance of aircraft, ensuring adequate lift at all flight stages.
- Wing aerodynamic performance assessment
- Stall speed determination and margin calculation
- Design and evaluation of high‑lift devices
- Airfoil selection and optimisation
- Flight control system development (based on C_L‑α relation)
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