Compute an aircraft's wing loading (W/S) and its level-flight stall speed from weight, wing area, maximum lift coefficient, and air density. Wing loading is one of the most important parameters in aircraft design β it sets stall and landing speeds, ride quality, and maneuverability. All inputs and outputs are SI.
Wing loading β the aircraft weight divided by its wing area, W/S β is a single number that captures much of an aircraft's character. It governs how fast the aircraft must fly to stay airborne, how it rides through turbulence, how tightly it can turn, and how short a runway it needs. This calculator returns wing loading directly and uses it to find the 1-g stall speed, the minimum speed at which the wing can still generate enough lift to support the aircraft.
Wing loading is simply W/S, the weight carried per unit of wing area. In steady level flight lift equals weight, and lift is L = Β½Β·ΟΒ·VΒ²Β·SΒ·C_L. Setting L = W and using the maximum achievable lift coefficient C_Lmax gives the lowest speed at which level flight is possible β the stall speed:
V_stall = β( 2Β·(W/S) / (ΟΒ·C_Lmax) )
Everything in this formula except W/S is either a property of the air (Ο) or of the wing (C_Lmax), which is why wing loading is the controlling design variable. Higher wing loading means a higher stall speed.
Because V_stall depends on the square root of wing loading, the relationship is gentle but unavoidable: to halve stall speed you must reduce wing loading to one-quarter, and quadrupling wing loading only doubles stall speed. A light trainer might have a wing loading of 50β80 kg/mΒ² and stall around 25 m/s, while an airliner near 600 kg/mΒ² stalls far faster and relies on powerful high-lift devices to keep approach speeds manageable. The same β relationship means stall speed also rises with the square root of load factor in a turn, V_s,turn = V_stallΒ·βn.
Low wing loading (a big wing for the weight) gives low stall and landing speeds, short field performance, good low-speed handling, and the ability to turn tightly β but a large wing adds weight and drag and makes the aircraft bounce around in gusts. High wing loading gives a smoother ride in turbulence and lower cruise drag, but demands higher takeoff, approach, and landing speeds and longer runways. Fighters, airliners, and gliders sit at very different points on this spectrum precisely because their missions value these factors differently.
The maximum lift coefficient C_Lmax sets how much lift a wing can produce before the flow separates and it stalls. A plain airfoil might reach C_Lmax β 1.3β1.5, but flaps and slats β high-lift devices deployed for takeoff and landing β can push it to 2.5 or higher. Because stall speed varies as 1/βC_Lmax, raising C_Lmax is the most effective way to bring a heavily-loaded wing's approach speed down. That is why airliners extend large multi-element flaps on final approach: it lets a high-wing-loading aircraft land safely at a reasonable speed.
It varies enormously by mission. Hang gliders and ultralights are around 10β30 kg/mΒ²; light general-aviation aircraft 50β100 kg/mΒ²; business jets 300β450 kg/mΒ²; large airliners 500β750 kg/mΒ². Higher wing loading trades short-field and low-speed performance for a smoother ride and lower cruise drag.
The formula assumes lift equals weight at a load factor of 1 g, which is straight-and-level flight. In a banked turn the wing must support more than the weight (load factor n > 1), so the stall speed rises by βn. The calculator reports the clean 1-g reference stall speed; multiply by βn for an accelerated stall in a turn.
Stall speed varies as 1/βΟ, so the thinner air at altitude or on a hot, high-altitude day raises the true airspeed needed to stay airborne. That is why field elevation and temperature matter so much for takeoff and landing performance. Using sea-level density (1.225 kg/mΒ³) gives the stall speed at standard sea-level conditions.
Enter weight as a force in newtons (mass in kg Γ 9.80665). The calculator reports W/S in N/mΒ² and also converts it to kg/mΒ² for convenience, the unit pilots and designers most often quote. If you only know mass in kilograms, multiply by 9.81 to get the weight in newtons first.
Flaps and slats raise C_Lmax, and since V_stall β 1/βC_Lmax, increasing C_Lmax lowers stall speed. Enter the clean C_Lmax for the clean stall speed (V_S) and the flaps-down C_Lmax for the landing-configuration stall speed (V_S0). The difference is exactly why high-lift devices exist.