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Aerospace

Stall speed in level flight

Slowest speed at which a wing can still carry the aircraft’s weight.

Ref: AER-05
Rev: v1
Field: Aerospace
Result: V_s [m/s]

V_{s} = \sqrt{\frac{2 W}{ρ S C_{L,max}}}

V_s in m/s, weight W = mg in newtons, ρ air density, S wing area and C_L,max the maximum lift coefficient for the aircraft’s configuration.

At the slowest flyable speed the wing is at its maximum lift coefficient. Setting lift equal to weight at that point gives the stall speed. Heavier aircraft stall faster; bigger wings and flaps lower it.

Calculator

Solve for

V_sStall speedComputed

m/s

mAircraft mass

20050,000

SWing area

m²

1100

C_L,maxMaximum lift coefficient

ρAir density

kg/m³

0.41.3

Stall speed in knots50.67 kt
Approach speed (1.3 V_s)33.89 m/s

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Stall speed (m/s) current value 26.07 m/s

mAircraft massKey driver

11.1176

SWing area

10.5105

ρAir density

25.345.6

C_L,maxMaximum lift coefficient

1933

Landing speed is usually set at about 1.3 times the stall speed for a safety margin.
Because of the square root, halving the stall speed needs four times the wing area or C_L,max.
In a banked turn the load factor n raises stall speed by √n, e.g. 7% at 30° bank.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (m/s)	Local step	Change in result
m Aircraft mass	200 to 50,000 kg	11.11	175.7	164.6	+10%	+4.88 %
S Wing area	1 to 100 m²	10.49	104.9	94.42	+10%	−4.65 %
ρ Air density	0.4 to 1.3 kg/m³	25.3	45.62	20.31	+10%	−4.65 %
C_L,max Maximum lift coefficient	1 to 3	19.04	32.97	13.94	+undefined%	—

Sweep of Aircraft mass

Aircraft mass (kg)	Stall speed (m/s)
200	11.11
398.8	15.7
795.3	22.16
1,586	31.3
3,162	44.2
6,306	62.41
12,570	88.13
25,070	124.5
50,000	175.7

Sweep one variable

Vary

Stall speed (m/s)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

V_s

Stall speed

Result · m/s

What the equation gives you. Everything else feeds it.

Aircraft mass

kg · typical 200 to 50,000

Total mass; the weight is mg. Stall speed rises with √m: 20% more mass gives about 10% higher stall speed.

Wing area

m² · typical 1 to 100

Reference wing area. Falls with √S.

C_L,max

Maximum lift coefficient

· typical 1 to 3

1.2–1.6 for clean wings, 2–3 with flaps. Falls with √C_L,max. Flaps are the practical route to lower stall speed.

Air density

kg/m³ · typical 0.4 to 1.3

Density at the flight altitude. Stall speed rises as the air thins (true airspeed).

Worked example with the values above

Weight: W = mg = 1,100 × 9.80665 = 10,790 N.
Inside the root: 2W / (ρSC_L,max) = 21,570 / 31.75 = 679.5 m²/s².
V_s = √679.5 = 26.07 m/s.

Assumptions and limits

Steady, unbanked level flight with lift equal to weight.
C_L,max valid for the actual configuration.
True airspeed; indicated airspeed differs with altitude.

Common mistakes

Using sea-level density at altitude for true airspeed.
Using clean C_L,max with flaps down.
Ignoring the weight change as fuel burns.

Statistics and uncertainty

The square root halves relative errors: δV/V ≈ ½ √[(δm/m)² + (δS/S)² + (δC_L/C_L)² + (δρ/ρ)²]. The largest uncertainty is usually C_L,max, which varies with surface condition, Reynolds number and flap setting (±5–10%).

Where it is used

Take-off and landing speeds.
UAV and missile launch speed limits.
Sizing wings for low-speed capability.

Maths you need

Lift equation: L = ½ρV²SC_L
Weight: W = mg

Related formulas

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