Turn inputs
Set your known values
Required fields change with the selected calculation mode.
Formula Used
Centripetal acceleration: ac = v² / r
Lateral g: glat = ac / g0
Coordinated bank relation: tan(φ) = v² / (r × g0)
Total load factor: n = 1 / cos(φ) = √(1 + glat²)
Turn rate: ω = v / r radians per second.
Here, v is speed in meters per second, r is radius in meters, g0 is reference gravity, and φ is bank angle. These equations apply to a steady, level, coordinated turn. They do not model climb, descent, drift, traction loss, or changing speed.
How to Use This Calculator
- Choose the input pair that matches your known values.
- Enter speed, radius, bank angle, or lateral g as required.
- Select the correct units before calculating.
- Keep reference gravity at 9.80665 m/s² for Earth calculations.
- Set a practical g limit for a visible warning.
- Review load factor, bank angle, radius, and turn rate together.
Example Data
| Known inputs | Value | Calculated outcome |
|---|---|---|
| Speed and radius | 180 km/h and 300 m | About 0.85 lateral g, 40.4° bank, and 1.31 g load factor. |
| Speed and bank angle | 120 knots and 30° | About 673 m radius, 0.58 lateral g, and 1.15 g load factor. |
| Radius and bank angle | 150 m and 45° | About 138 km/h speed, 1.00 lateral g, and 1.41 g load factor. |
G-Force Turn Fundamentals
A g-force turn describes the acceleration experienced while an object follows a curved path. It helps judge comfort, structural loading, traction, and human tolerance. A turn can feel demanding at moderate speed. The important variables are speed, radius, and bank angle. Smaller radii increase acceleration quickly. Higher speeds increase it even faster. This calculator keeps those relationships visible.
In a level coordinated turn, the support force tilts inward. Its horizontal part supplies centripetal acceleration. The result is a load factor greater than one. A one g load factor means straight, level motion. A two g load factor means the support force is twice normal weight. This matters because lateral acceleration and total load factor are not identical.
The speed and radius mode is useful when a route or track is known. Enter path radius and current speed. The calculator finds centripetal acceleration, lateral g, bank angle, load factor, and turn rate. Results assume constant speed and a smooth circular path.
The speed and bank mode is common for aircraft planning. Enter true speed and a chosen bank angle. The result shows the radius needed for a level coordinated turn. Steeper banks reduce turn radius. They raise load factor sharply. Do not use a ninety degree bank. Support requirements become unbounded near that angle.
The radius and bank mode solves for the speed that fits both conditions. The speed result is theoretical. It does not confirm engine power, tire grip, stall margin, surface condition, or structural approval. Treat it as a kinematic starting point. Add operating limits before making decisions. This is prudent.
Lateral g is centripetal acceleration divided by standard gravity. Load factor is combined support acceleration. In a coordinated turn, load factor equals reciprocal cosine bank angle. It also equals the square root of one plus lateral g squared. Expressions agree when assumptions are satisfied. Differences suggest input error, a nonlevel turn.
Choose the input mode first. Then enter only required values. Select units carefully. Add a practical g limit for a warning. This limit can represent pilot comfort, passenger comfort, tire capability, or a design target. The calculator flags values above it. It does not replace manuals, engineering review, or professional instruction.
Use the result panel above the form to compare scenarios quickly. Record bank angle and load factor together. Review radius and turn rate as a pair. A fast turn rate can require a wide path. A small radius can feel gentle at low speed. Export results as CSV for notes or testing. Use print to save a browser PDF.
This tool models ideal constant-speed turns. Wind, slope, vertical motion, skid, slip, suspension movement, road banking, and changing radius alter forces. Aircraft results require coordinated level flight. Vehicle results need traction analysis. Human tolerance depends on duration and direction. Leave sensible margins. Reduce speed when conditions are uncertain. Confirm critical limits using approved references and qualified advice.
Common questions
G-Force Turn FAQs
What is g-force in a turn?
It is acceleration relative to standard gravity while following a curved path. This page reports lateral g and total load factor separately, because they describe different aspects of the turn.
Is lateral g the same as load factor?
No. Lateral g measures inward turning acceleration. Load factor measures total supporting acceleration in a level coordinated turn. At one lateral g, total load factor is about 1.41 g.
Why does speed raise g-force quickly?
Centripetal acceleration uses speed squared. Doubling speed at the same radius produces four times the lateral acceleration. This is why modest speed changes can strongly affect a tight turn.
Can I use this for aircraft?
Yes, for an ideal level coordinated turn. Use true airspeed when possible. Check aircraft performance data, stall limits, maneuvering limits, and operating procedures separately before relying on the result.
Can I use this for cars or motorcycles?
Yes, as a basic curved-motion estimate. Real road vehicles also depend on tire grip, surface condition, suspension, road banking, braking, and steering inputs. The calculator does not predict traction loss.
Which speed should I use?
Use the actual speed through the turn. For aviation, true airspeed is usually the best starting point. For ground vehicles, use speed relative to the road path.
What bank angle should I enter?
Enter the planned or measured bank angle from level. Keep it below 89.9 degrees. Higher bank angles create rapidly increasing load factors and unrealistic requirements.
Why is a 90-degree bank excluded?
At 90 degrees, cosine bank angle becomes zero. The ideal level-turn equation therefore requires infinite load factor. Real aircraft and vehicles cannot maintain that condition.
What does turn rate mean?
Turn rate is the heading change per second. A larger rate completes a circle faster. It should be considered with radius, speed, and load factor, not alone.
Why did I receive a warning?
Warnings appear for high bank angles, high calculated load factors, or a result above your chosen practical limit. They are prompts to review inputs and real-world operating limits.
Does this include weather or traction?
No. It uses an ideal constant-speed model. Wind, road conditions, tire friction, vertical motion, and changing radius can alter real forces substantially.