Lift Force Calculator
Work out the lift a wing makes — solve for lift, air density, airspeed, lift coefficient or wing area, derive density from altitude, and check stall speed, drag and lift-to-drag in Advanced mode.
Lift grows with the square of airspeed: doubling speed quadruples lift. The teal curve uses your lift coefficient, the dashed amber curve uses CL,max (the most lift the wing can make before it stalls), and the red dot is your operating point.
Lift acts perpendicular to the relative wind and drag acts along it. The angle between the chord line and the relative wind is the angle of attack α, which together with the wing shape sets CL. In steady level flight lift balances weight.
| Altitude | Density ρ |
|---|---|
| 0 m (sea level) | 1.225 kg/m³ |
| 1,000 m | 1.112 kg/m³ |
| 2,000 m | 1.007 kg/m³ |
| 3,000 m | 0.909 kg/m³ |
| 5,000 m | 0.736 kg/m³ |
| 10,000 m | 0.414 kg/m³ |
| Condition | CL (approx.) |
|---|---|
| Cruise, clean wing | 0.2 – 0.6 |
| Maximum, flaps up | 1.2 – 1.8 |
| Maximum, flaps down (landing) | 2.0 – 3.0 |
| Symmetric section at zero angle | ≈ 0 |
| Quantity | Relation |
|---|---|
| Speed | 1 kt = 0.5144 m/s · 1 mph = 0.4470 m/s · 1 km/h = 0.2778 m/s |
| Force | 1 lbf = 4.4482 N · 1 kN = 1,000 N |
| Area | 1 ft² = 0.09290 m² |
| Density | 1 slug/ft³ = 515.38 kg/m³ |
Airspeed v
Lift scales with v², the strongest lever. A 10% faster wing makes about 21% more lift.
Air density ρ
Thin air at altitude or on a hot day cuts lift in proportion, so you need more speed, area or CL to hold the same weight.
Lift coefficient CL
CL rises with angle of attack and flap setting until the wing stalls at CL,max, after which lift falls away.
Wing area A
Lift is directly proportional to area. More area lowers wing loading and the stall speed, at the cost of weight and drag.
What Is Lift Force?
Lift is the aerodynamic force that acts perpendicular to the oncoming airflow on a wing, blade or other lifting surface. It comes from the wing deflecting air downward and from the pressure difference between its upper and lower surfaces. In steady level flight, lift equals the aircraft's weight.
The Lift Force Formula
The term ½ρv² is the dynamic pressure q, the kinetic energy of the airflow per unit volume. Multiplying it by the wing area A gives the force scale, and the dimensionless lift coefficient CL captures everything about the wing's shape, angle of attack and flap setting. The formula assumes smooth, essentially incompressible flow, so it is most accurate below about Mach 0.3.
How to Calculate Lift Force
Choose the unknown above, enter the other four values with their units, and the calculator converts to SI and rearranges the formula. All inputs must be greater than zero.
| Solve for | Rearranged formula |
|---|---|
| L | L = ½ · ρ · v² · CL · A |
| ρ | ρ = 2L / (v² · CL · A) |
| v | v = √( 2L / (ρ · CL · A) ) |
| CL | CL = 2L / (ρ · v² · A) |
| A | A = 2L / (ρ · v² · CL) |
Lift Force Formula Variables
| Symbol | Meaning |
|---|---|
| L | Lift force, in newtons |
| ρ | Air density, in kg/m³ |
| v | True airspeed relative to the wing, in m/s |
| CL | Lift coefficient (dimensionless) |
| A | Wing planform area, in m² |
| q, W | Dynamic pressure ½ρv² and weight (derived, not entered) |
Air Density and Altitude
Air gets thinner as you climb and as it warms, so the same wing makes less lift at the same speed. Turn on the density option in Advanced mode and enter an altitude to compute ρ from the International Standard Atmosphere, with an optional temperature offset for hot or cold days. At 3,000 m the density is about 74% of sea level, so the same lift needs roughly 16% more airspeed.
Stall Speed and the Lift Coefficient
A wing cannot raise its lift coefficient forever. Past a critical angle of attack the flow separates and the wing stalls, so CL tops out at CL,max. In level flight, lift equals weight, which gives the stall speed Vs = √(2W / (ρ · A · CL,max)). Enter CL,max in Advanced mode to see it, and a drag coefficient CD to get drag and the lift-to-drag ratio.
Lift Force Calculation Example
q = ½ × 1.225 × 50² = 1,531 Pa
L = 1,531.25 × 0.4 × 16.2 = 9,922.5 N ≈ 9.92 kN → supports about 1,012 kg
With CL,max = 1.6, stall speed Vs = 50 × √(0.4 / 1.6) = 25 m/s (about 49 kt)
Frequently Asked Questions
Two things grow with speed. The wing meets more air per second, and each parcel of air is deflected with more momentum. Together they give a force proportional to v², which is why dynamic pressure ½ρv² is the natural scale.
Use true airspeed with the actual local air density. If you only know indicated airspeed, which is calibrated to sea-level density, enter sea-level density (1.225 kg/m³) with it instead, since the two corrections cancel.
It assumes incompressible air. Above roughly Mach 0.3, compressibility changes how pressure and density vary over the wing, and near the speed of sound shock waves change CL and drag strongly. The badge on the result card flags when your speed is in that range.
Flaps increase both the wing's camber and effective area, raising CL and CL,max. That lets the same weight fly at a lower speed, so stall speed drops with flaps down. Use the CL value that matches the flap setting you are analysing.
The same relation holds for any lifting surface in a flow, but v must be the local relative speed over that surface. For a rotor blade that varies along its length, so you would integrate over the span rather than use one speed and one area.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| L | Lift force | N |
| ρ | Air density | kg/m³ |
| v | Velocity | m/s |
| C_L | Lift coefficient | |
| A | Wing area | m² |
What it means
The lift equation is the fundamental formula for calculating the lift force generated by an aerodynamic surface (such as a wing) in a fluid flow. It states that lift is proportional to the dynamic pressure (½ρv²), the planform area, and the lift coefficient (which depends on angle of attack and airfoil shape). This equation is derived from Bernoulli’s principle and the conservation of momentum. It is used extensively in aircraft design to determine required wing area for a given weight, to predict performance at various speeds, and to assess load factors. The lift coefficient C_L is typically obtained from wind tunnel tests or computational fluid dynamics (CFD). In flight mechanics, the lift equation is central to understanding takeoff, landing, stall, and manoeuvring. It also applies to rotorcraft, wind turbines, and even sports equipment like golf balls and aerofoils. Engineers use it to optimise wing designs for efficiency and safety. Understanding this equation is essential for aerospace engineers and pilots to interpret flight performance.
Worked example
Lift Equation – Two Additional Examples
Real‑World| Parameter | Value |
|---|---|
| ρ | 0.36 kg/m³ |
| V | 250 m/s |
| C_L | 0.52 |
| S | 541 m² |
| Parameter | Value |
|---|---|
| ρ | 1.225 kg/m³ |
| V | 50 m/s |
| C_L | 0.65 |
| S | 16.2 m² |
Common mistakes
- Lift equation: L = ½ρv²C_L·A uses dynamic pressure (q = ½ρv²). Ensure ρ is in kg/m³, v in m/s, A in m² → L in Newtons.
- Lift coefficient C_L: Depends on angle of attack, airfoil shape, and Reynolds number – not constant. Use proper aerodynamic data.
- Air density ρ: Varies with altitude; use standard atmosphere or local conditions.
- Reference area A: Usually wing planform area – not the wetted area.
- Angle of attack: This equation gives lift for a given α; C_L is not linear over the entire range (stall occurs).
Applications
The lift equation, L = ½ρV²C_L·A, is the fundamental relationship that quantifies the aerodynamic lift generated by a wing or airfoil. It states that lift is proportional to air density, the square of velocity, the wing area, and the lift coefficient. This equation is the cornerstone of aircraft design, enabling engineers to size wings, determine takeoff and landing speeds, and optimise performance across the flight envelope. In practice, it is used to calculate the lift generated at various angles of attack, to design high‑lift devices (flaps, slats), and to predict stall conditions. The lift equation also applies to rotorcraft, wind turbines, and even racing cars (where it is used as downforce). By mastering this formula, aerospace engineers can ensure that aircraft have sufficient lift to support their weight while minimising drag, thereby achieving safe and efficient flight.
- Wing sizing and design for aircraft
- Determination of takeoff and landing speeds
- Design of high‑lift devices (flaps, slats, leading‑edge devices)
- Stall speed and margin calculations
- Application to wind turbines, rotorcraft, and automotive aerodynamics
Related calculators · Aerodynamics
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.