Rotating Habitat Gravity Gradient Calculator
Estimate head-to-foot artificial-gravity gradient and rotation rate inside a rotating space habitat.
Last reviewed: June 2026What this calculator is modeling
This calculator is for rotating space habitats, not terrestrial flow models. A rotating cylinder, wheel, torus, or tethered spacecraft can create artificial gravity at the outer floor because an occupant must follow a circular path. The basic relationship is g = omega^2 r, where omega is angular speed in radians per second and r is the floor radius from the spin axis.
The calculator solves that relationship from your target gravity and radius, then reports the rotation rate in RPM. It also estimates the head-to-foot gravity gradient by comparing acceleration at the feet with acceleration at the head. Because the head is closer to the spin axis, it feels slightly less artificial gravity than the feet.
Inputs and assumptions
Cylinder Radius is the distance from the rotation axis to the floor in meters. Person Height is the radial distance from the feet to the head. Target Gravity at Feet is the acceleration you want at the floor, such as 9.81 m/s2 for Earth-like gravity or lower values for partial-gravity studies.
The model assumes a simple circular habitat with the person standing radially, feet outward and head inward. It does not calculate moving-person Coriolis force, cross-coupled vestibular response, structural stress, spin-up transients, or habitat stability. Use the RPM and gradient outputs as screening numbers before deeper design work.
Worked examples
With the default 3,200 m radius, 1.8 m person height, and 9.81 m/s2 target gravity, the calculator reports a gravity gradient of 0.0563%. The head gravity is about 9.8045 m/s2, the difference is about 0.0055 m/s2, and the station rotates at about 0.5287 RPM. That is the kind of low-gradient result expected from very large O'Neill-style habitat concepts.
At a 100 m radius with the same height and floor gravity, the gradient rises to 1.8000% and the rotation rate rises to about 2.9909 RPM. At a 10 m radius, the gradient becomes 18.0000% and the required rotation rate is about 9.4581 RPM, making the head-to-foot difference and motion-adaptation concerns much more prominent.
How to interpret the outputs
- Gravity Gradient: the head-to-foot difference as a percentage of floor gravity. Larger habitats reduce this number.
- Gravity at Feet: the target floor acceleration, useful for comparing Earth, Mars, Moon, or custom partial-gravity levels.
- Gravity at Head: the artificial gravity at a point one body height closer to the axis.
- g Difference: the absolute head-to-foot difference in m/s2.
- Rotation Rate: the RPM needed to produce the selected floor gravity at the selected radius.
Design tradeoffs
Increasing radius helps twice: it lowers the head-to-foot gradient and lowers the RPM needed for a given target gravity. That is why large settlement studies often favor kilometer-scale radii. Smaller centrifuges can still be useful for exercise, research, or short-duration countermeasures, but they usually require more attention to adaptation, body motion, and operational limits.
Lowering target gravity also lowers the rotation rate for a fixed radius. A Mars-like or lunar-like setting can therefore be less demanding than full Earth gravity, although the biological sufficiency of partial gravity remains a separate question. This calculator only gives the kinematic numbers; it does not answer long-term physiology.
Common mistakes
- Using terrestrial Coriolis examples: planet-scale flows are not what this page calculates.
- Looking only at gradient: a low head-to-foot gradient can still come with an RPM that is uncomfortable for some body motions.
- Treating comfort bands as medical limits: adaptation varies, and real human-factors work needs testing and mission context.
- Ignoring structure and dynamics: a radius/RPM pair says nothing about pressure vessel design, bearing loads, shielding, or stability.
Sources
This page is aligned with NASA NTRS material on Physics of Artificial Gravity, NASA's overview of artificial gravity, and the NASA SP-413 Space Settlements: A Design Study.