Enter the total lift force (often equal to the aircraft’s weight in steady level flight), air density, coefficient of lift (use CL,max for stall), and wing surface area into the calculator to determine the stall speed of an aircraft.
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Stall Speed Formula
Stall speed is the lowest airspeed at which an aircraft, in a specific configuration and load factor, reaches the wing’s critical angle of attack and can no longer produce enough lift for steady flight. The stall itself is caused by angle of attack, not by a single fixed speed, which is why stall speed changes with weight, flap setting, bank angle, icing, and air density.
V_s = \sqrt{\frac{2L}{C_{L,\max}\rho S}}In steady 1g level flight, required lift is usually equal to aircraft weight, so the same relationship is often written as:
V_s = \sqrt{\frac{2W}{C_{L,\max}\rho S}}| Variable | Meaning | Typical Notes |
|---|---|---|
| Vs | Stall speed | Usually discussed in IAS for aircraft operations |
| L | Required lift force | In straight-and-level 1g flight, this is typically equal to weight |
| W | Aircraft weight | Use force units such as N or lbf |
| CL,max | Maximum lift coefficient | Use the value for the actual configuration at stall |
| ρ | Air density | Changes with altitude, temperature, and pressure |
| S | Wing planform area | Use the lifting surface area assumed by the aircraft data |
Rearranging the Equation
If you know four values, the calculator can solve for the fifth. These are the most useful rearrangements:
L = \frac{V_s^2 C_{L,\max}\rho S}{2}C_{L,\max} = \frac{2L}{V_s^2 \rho S}\rho = \frac{2L}{V_s^2 C_{L,\max} S}S = \frac{2L}{V_s^2 C_{L,\max}\rho}How to Use the Stall Speed Calculator
- Enter lift force or weight. In steady, unaccelerated level flight, required lift is normally equal to the aircraft’s weight.
- Enter the maximum lift coefficient. Use CL,max for the exact configuration being analyzed, such as clean, takeoff flap, or landing flap.
- Enter air density. Density falls as altitude increases and also changes with temperature and pressure.
- Enter wing area. Use wing planform area, keeping units consistent with the rest of the calculation.
- Calculate the missing value. The output stall speed will be valid only for the entered conditions.
Unit tip: Keep the entire equation in one unit system. For SI, use N, kg/m3, and m2. For imperial, use lbf, slugs/ft3, and ft2. If you use pounds for weight, enter pounds-force rather than pounds-mass.
What Changes Stall Speed?
| Change | Effect on Stall Speed | Why It Happens |
|---|---|---|
| Higher weight | Increases | More lift is required, so the wing must operate at a higher dynamic pressure before reaching CL,max. |
| Higher CL,max | Decreases | A wing that can make more lift before stalling can fly slower before reaching the critical angle of attack. |
| Lower air density | Raises stall TAS | Thin air requires more true speed to create the same lift. |
| Larger wing area | Decreases | More lifting surface reduces the speed needed to support the aircraft. |
| Higher load factor | Increases | Turning or pulling G increases required lift above simple 1g weight support. |
| Ice, contamination, or damage | Usually increases | These conditions often reduce attainable CL,max and disturb airflow over the wing. |
Useful Stall Speed Relationships
Two of the most important real-world changes are weight and load factor.
V_{s,2} = V_{s,1}\sqrt{\frac{W_2}{W_1}}This means stall speed changes with the square root of weight. A 21% increase in weight produces about a 10% increase in stall speed.
V_{s,n} = V_{s,1g}\sqrt{n}In maneuvering flight, load factor n raises the stall speed above the normal 1g value. In a coordinated level turn, load factor depends on bank angle:
n = \frac{1}{\cos \phi}At a 60° bank, the load factor is 2, so stall speed becomes about 1.414 times the 1g stall speed.
Altitude, IAS, and TAS
For the same aircraft weight and configuration, stall speed in indicated airspeed is nearly constant because indicated airspeed reflects the dynamic pressure acting on the wing. True airspeed at the stall increases as density decreases.
V_{s,TAS} \propto \frac{1}{\sqrt{\rho}}That is why an aircraft may stall at roughly the same indicated airspeed at sea level and at altitude, while the actual speed through the air is higher at altitude.
Example Calculation
If the required lift is 9,800 N, the maximum lift coefficient is 1.5, the air density is 1.225 kg/m3, and the wing area is 16.2 m2, then:
V_s = \sqrt{\frac{2(9800)}{1.5(1.225)(16.2)}} \approx 25.66 \text{ m/s}This corresponds to a stall speed of about 49.9 knots.
Practical Notes
- Use CL,max for the exact aircraft configuration. Flaps, slats, and other high-lift devices can change stall speed significantly.
- The equation is most useful as a clean aerodynamic estimate. Published aircraft handbook values should always take priority for actual operation.
- Wing contamination, turbulence, and maneuvering can make the effective margin above stall smaller than the simple 1g calculation suggests.
- A stall can occur at any airspeed if the wing exceeds its critical angle of attack.
FAQ
Does higher weight increase stall speed?
Yes. Heavier aircraft need more lift, so the wing must fly at a higher airspeed before reaching the maximum usable lift coefficient.
Do flaps reduce stall speed?
Usually yes. Flaps generally increase CL,max, which lets the wing support the aircraft at a lower airspeed before stalling.
Does stall speed increase with altitude?
It increases in true airspeed, but for the same weight and configuration it remains nearly the same in indicated airspeed.
Can an airplane stall above the published stall speed?
Yes. Published stall speeds are typically based on specific configurations and load factors. Banking, pulling G, or abrupt control inputs can cause a stall at a much higher airspeed.
