What is a coordinated turn?

A turn where the aircraft's bank angle is matched to its speed and radius so there is no sideslip — the ball in the turn-and-slip indicator stays centred.

Why does load factor increase with bank angle?

The vertical component of lift must still support weight, so total lift (and load factor) must increase as the wing tilts.

What bank angle causes 2 g?

60° of bank produces a load factor of exactly 2 g in a coordinated turn.

How does speed affect the turn?

At higher speed, a larger radius or steeper bank is needed; turn rate actually decreases for a given bank angle as speed increases.

Can a car bank like an aircraft?

On a banked road, yes. The road tilt replaces wing-generated lift for the horizontal force component.

What is the maximum bank angle for airliners?

Commercial airliners are typically limited to 25–30° bank. Emergency manoeuvers may use up to 45°.

Bank Angle Calculator

Calculate bank angle, turn radius, load factor, and turn rate for aircraft or vehicles in coordinated turns. Includes G-force and stall speed factor.

Presets

Solve For

Speed (km/h)

Turn Radius (m)

Aircraft Weight (kg)

Altitude (m)

Bank Angle

13.81°

Angle of bank required for coordinated turn

Turn Radius

2,000 m

Radius of the circular flight path

Load Factor (G)

1.03 g

Apparent weight multiplier on aircraft and occupants

Turn Rate

1.99°/s

Angular rate of heading change

Time per 360°

181.0 s

Time to complete a full circle

Stall Speed Factor

×1.01

Multiply level-flight stall speed by this factor in the turn

Centripetal Force

168.8 kN

Inward force on the aircraft

Lift Required

707.1 kN

Total lift to sustain the banked turn

G-Force Indicator

Bank Angle vs Speed (constant radius 2,000.00 m)

Speed (km/h)	Bank (°)	Load (g)	Turn Time (s)
80	1.4	1.00	565.5
120	3.2	1.00	377.0
200	8.9	1.01	226.2
300	19.5	1.06	150.8
400	32.2	1.18	113.1
500	44.5	1.40	90.5

Bank Angle vs G-load

Bank (°)	Load Factor (g)	Stall Factor	Radius (m)
10	1.02	×1.01	2,788
20	1.06	×1.03	1,351
30	1.15	×1.07	851
45	1.41	×1.19	492
60	2.00	×1.41	284
75	3.86	×1.97	132
80	5.76	×2.40	87

Planning notes, formulas, and examples

About the Bank Angle Calculator

The **Bank Angle Calculator** computes the geometry and forces of a coordinated (constant-altitude) banked turn. Given speed and turn radius, it finds the required bank angle; or given bank angle and speed, it finds the resulting radius. It also calculates load factor (g), turn rate, time to complete 360°, centripetal force, and the stall-speed increase in the turn.

Banked turns appear everywhere: aircraft, racecars, motorcycles, and even banked roads. The physics is the same — the horizontal component of the lift (or friction) force provides the centripetal acceleration needed for circular motion. As the bank angle increases, so does the load factor and the stall speed, making steep turns more dangerous.

Use the built-in aircraft presets or enter custom values. The reference tables show how bank angle, G-force, and radius interact across a range of speeds and angles, making this an invaluable tool for pilots, automotive engineers, and physics students.

When This Page Helps

Whether you are a pilot planning a holding pattern, an engineer designing a banked curve, or a student studying circular motion, this calculator delivers the full set of turn aerodynamics and forces.

How to Use the Inputs

Choose whether to solve for bank angle (given radius) or turn radius (given angle).
Enter speed in km/h.
Enter turn radius in metres or bank angle in degrees, depending on the mode.
Set the aircraft or vehicle weight for force calculations.
Optionally select a preset for quick values.
Read bank angle, load factor, turn rate, stall factor, and forces.
Consult the reference tables for design comparisons.

Formula used

Bank Angle: φ = arctan(v² / (g R))
Turn Radius: R = v² / (g tan φ)
Load Factor: n = 1 / cos φ
Turn Rate: ω = g tan φ / v  [rad/s]
Stall Speed Factor: √n

where v = speed, g = 9.81 m/s², R = radius, φ = bank angle.

Example Calculation

Result: 14.0° bank, 1.031 g load factor, 133 s per 360°

A Boeing 737-class aircraft at 250 km/h in a 2 km radius turn needs about 14° of bank, experiencing 1.03 g — barely noticeable to passengers.

Tips & Best Practices

At 60° bank, stall speed increases by 41% — add speed margin accordingly.
Standard-rate turns (3°/s) at 120 kts require about 25° of bank.
For cars on flat roads, friction replaces lift; the "bank angle" is effectively zero.
G-load limits for utility-category aircraft are typically +3.8 g / −1.52 g.
Use the speed-vs-angle table to find the minimum-radius turn your vehicle can safely execute.

When To Use This Calculator

Calculate bank angle, turn radius, load factor, and turn rate for aircraft or vehicles in coordinated turns. Includes G-force and stall speed factor. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

A turn where the aircraft's bank angle is matched to its speed and radius so there is no sideslip — the ball in the turn-and-slip indicator stays centred.