Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

Gravitational Parameter Cubic Meters Per Second Squared (m³/s²)

Required number input.

Radius Meters (m)

Required number input.

Ideal two-body escape speed √(2μ/r) at a specified center-to-center radius; ignores atmosphere and rotation. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Escape Meters Per Second (m/s)

The resulting escape meters per second returned as a number.

• Simple orbital speed and escape formulas assume idealized point or spherical masses and often neglect atmosphere, rotation, nonspherical gravity, other bodies, propulsion losses, and the distinction between local speed and mission delta-v.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Horizontal Curve Radius

  Minimum ideal level-curve radius for specified speed and combined superelevation plus lateral friction: R=v²/[g(e+f)].

• Orbital Velocity

  Circular-orbit speed √(μ/r) around a central body from its gravitational parameter and distance from its center.

• Battery SOC Coulomb

  Ideal battery state of charge after a constant discharge current, using nominal amp-hour capacity; ignores coulombic losses and aging.