What stall speed is, and what it is not
A wing stalls at an angle of attack, not at a speed. The stall speed is simply the slowest speed at which the wing can still produce enough lift to support the aircraft while operating at that critical angle. Push the angle of attack past the critical value at any speed and the wing stalls; the number this calculator produces is the speed at which you have no choice but to reach that angle, because there is no slower speed at which the lift still balances the weight.
That distinction matters because it explains every way stall speed changes. Anything that raises the required lift — more weight, more load factor in a turn or a pull-up — raises the speed at which the critical angle is reached. Anything that raises the wing's maximum coefficient — flaps, slats, a clean leading edge instead of an iced one — lowers it. Nothing about the air itself changes the calibrated stall speed, which is why a published VS1 holds at every altitude.
Stall speed is the reference from which most of the other speeds on the airspeed indicator are derived. Under 14 CFR Part 23 certification practice, the bottom of the white arc is VS0, the stall speed in the landing configuration, and the bottom of the green arc is VS1, the stall speed clean. Approach speeds are built as a multiple of VS0, commonly 1.3 times, and best-angle and best-rate climb speeds sit well above it. Getting stall speed wrong propagates into all of them.
How the formula is built and what each term does
Start from level flight: lift must equal weight, so W = ½ρV²S·CL. Set CL to its maximum, rearrange for V, and you have the stall speed. Everything follows from that one rearrangement.
Weight enters under a square root, so stall speed scales with √W. Burning off 25% of your weight lowers the stall speed by only about 13%, because √0.75 = 0.866. This is also why the published stall speed at maximum gross weight is conservative for almost every real flight.
Wing area is in the denominator, so W and S always appear together as the ratio W/S. That ratio is the wing loading, and it is the only aircraft-specific quantity in the formula besides CLmax. Two completely different aircraft with the same wing loading and the same maximum coefficient stall at the same speed. The wing loading calculator gives the ratio directly.
CLmax is the configuration. Full flaps typically lift a light single's maximum coefficient from about 1.5 to about 2.0, which lowers the stall speed by √(1.5/2.0) = 0.866, or roughly 13%. That is the entire mechanical benefit of flaps for stall margin; the rest of their value is drag and approach path angle.
Density is fixed at the sea-level standard value in the primary result. This is deliberate. Using ρ0 produces equivalent airspeed, which is what the airspeed indicator approximates, and it is why stall warning systems and airspeed markings work unchanged at altitude. Substitute actual density and you get true airspeed at the stall, which rises about 2% per thousand feet of density altitude and is the reason a high-altitude go-around covers so much ground.
Load factor enters through the required lift. In a level turn the vertical component of lift must still equal weight, so total lift is W/cosφ and the load factor is n = 1/cosφ. Since stall speed scales with the square root of the required lift, it scales with √n. At 60° of bank n is exactly 2 and stall speed rises by 41.4%; at 45°, n is 1.414 and stall speed rises 19%.
Worked example: 2,400 lb, 174 ft², CLmax 1.5
Take a four-seat light single at 2,400 lb with 174 ft² of wing and a clean maximum lift coefficient of 1.5.
- Form the denominator. ρ0 × S × CLmax = 0.0023769 × 174 × 1.5 = 0.0023769 × 261 = 0.620368.
- Form the numerator. 2W = 2 × 2,400 = 4,800.
- Divide and take the root. 4,800 ÷ 0.620368 = 7,737.3, and √7,737.3 = 87.96 ft/s.
- Convert to knots. 87.96 ÷ 1.68781 = 52.12 kt calibrated. Sanity check: the wing loading is 2,400 ÷ 174 = 13.79 lb/ft², right in the range where light singles stall in the low fifties.
- Add a 30° bank. cos 30° = 0.86603, so n = 1.1547 and √n = 1.07457. Stall speed becomes 52.116 × 1.07457 = 56.00 kt.
- Try 60° instead. cos 60° = 0.5 exactly, so n = 2.000 and √2 = 1.41421. Stall speed becomes 52.116 × 1.41421 = 73.70 kt — a 21.6 kt increase over wings-level, achieved by a bank angle many pilots roll into without thinking.
- Land 600 lb lighter. At 1,800 lb, Vs = 52.12 × √(1,800 ÷ 2,400) = 52.12 × 0.86603 = 45.13 kt.
Finally, the altitude case. At 10,000 ft pressure altitude on a standard day (−4.8 °C) the density is 0.9046 kg/m³, giving a density ratio σ = 0.9046 ÷ 1.225 = 0.7384. The wing still stalls at 52.12 kt calibrated, but the true airspeed is 52.12 ÷ √0.7384 = 52.12 ÷ 0.8593 = 60.65 kt. Your turn radius at the stall grows with the square of that true airspeed, which is 35% larger than at sea level.
How to read the result
Compare it to the AFM, not the other way round. The number here is a clean aerodynamic calculation. Your AFM's published VS0 and VS1 come from flight test with a specific deceleration rate, a specific power setting and the actual position error of that airframe's static system. If your computed figure differs from the book by more than a couple of knots, the likely culprit is your assumed CLmax, which is rarely published and is usually back-calculated from the book stall speed in the first place.
Back out CLmax instead. The most useful way to use this page is inverted: take your AFM stall speed at gross weight, solve for the CLmax that reproduces it, then use that coefficient for every other weight, bank angle and flap setting. That removes the guesswork and makes the results specific to your aircraft.
Approach speed margins. A 1.3 VS0 approach at 45 kt landing-configuration stall speed is 58.5 kt. In a 30° turn onto final at that speed, the accelerated stall speed is 45 × 1.0746 = 48.4 kt, leaving 10 kt of margin. Steepen to 45° to correct an overshoot and the stall speed goes to 53.5 kt, cutting the margin in half. That is the mechanism behind the classic base-to-final stall, and the arithmetic is entirely visible in the bank angle table below.
Load factor thresholds. Normal-category aircraft under Part 23 are stressed to +3.8 g, utility to +4.4 g and aerobatic to +6.0 g. A level turn reaches 3.8 g at about 74.7° of bank. Above 2 g the calculator flags the loading, because that is where a stall becomes an accelerated stall with a much more abrupt break.
Load factor and stall speed multiplier by bank angle
| Bank angle | Load factor n = 1/cosφ | Stall speed multiplier √n | Vs at 52.12 kt base (kt) | Turn radius at 100 kt TAS (ft) |
|---|---|---|---|---|
| 0° | 1.000 | 1.000 | 52.12 | — |
| 15° | 1.035 | 1.017 | 53.03 | 3,304 |
| 30° | 1.155 | 1.075 | 56.00 | 1,534 |
| 45° | 1.414 | 1.189 | 61.98 | 885 |
| 60° | 2.000 | 1.414 | 73.70 | 511 |
| 70° | 2.924 | 1.710 | 89.12 | 322 |
| 75° | 3.864 | 1.966 | 102.44 | 237 |
Turn radius is V²/(g·tan φ) at 100 kt true airspeed (168.78 ft/s), shown to make the trade explicit: tightening the turn costs stall margin faster than it buys radius.
What this calculation leaves out
- Power effects. A propeller blowing over the wing raises the effective maximum coefficient, so a power-on stall in a light single occurs several knots slower than a power-off stall. Certification stall speeds are measured at idle for exactly this reason.
- Contamination. Frost, ice or even heavy insect accretion on the leading edge cuts CLmax substantially, and the loss is not proportional to the visible roughness. Any leading-edge contamination invalidates the published number.
- Centre of gravity. A forward CG needs more tail download, which the wing must offset with extra lift, so stall speed rises slightly. Use the weight and balance calculator to see where your loading sits; a forward-limit loading can add a knot or two.
- Rate of entry. A rapid deceleration produces a lower indicated stall speed than the 1 kt per second certification entry rate because of unsteady aerodynamic effects. Fast entries flatter the number.
- Position error. Near the stall the static port sees a distorted pressure field, so indicated airspeed can differ from calibrated by several knots. The AFM calibration table is the only way to convert reliably.
- Ground effect. Within about one wingspan of the surface, induced drag falls and the wing behaves as if it had a higher aspect ratio, which can lower the apparent stall speed during the flare.
Related speeds and where to go next
The manoeuvring speed VA is the direct child of this calculation: it is the speed at which the wing reaches CLmax exactly when the load factor reaches the design limit, so VA = VS1 × √nlimit. For a normal-category aircraft with a 52 kt clean stall and a 3.8 g limit, VA at gross weight is 52 × 1.949 = 101 kt. Because both VS1 and VA scale with √W, manoeuvring speed falls as the aircraft gets lighter — which is the opposite of what most pilots' intuition suggests, and it is why AFMs publish VA at several weights.
If you want to understand where CLmax comes from rather than treating it as an input, work with the lift equation calculator, which lets you solve for the coefficient your wing must reach at any speed and weight. For design work, wing loading and its cousin power loading, both available in the wing loading calculator, are the parameters that fix stall speed and climb performance before any aerofoil is chosen.
One historical note that illuminates the physics: the reason certification rules cap the stall speed of single-engine aircraft (61 kt for most, under the older Part 23 rules) is that impact energy scales with the square of speed. A 61 kt stall speed rather than an 80 kt one reduces the kinetic energy at a controlled forced landing by 42%, which is the single largest lever on survivability. Wing loading, and therefore this calculation, is what that rule really constrains.