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

Speed Meters Per Second (m/s)

Required number input.

Gravity Meters Per Second Squared (m/s²)

Required number input.

Superelevation Ratio

Required number input.

Lateral Friction Factor

Required number input.

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

Radius Meters (m)

The resulting radius meters returned as a number.

• Road geometry, pavement loading, sight distance, superelevation, and traffic estimates depend on jurisdictional criteria, design speed, vehicles, grade, friction, climate, drainage, growth, human factors, and survey data. Apply the current road authority standard.
• 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.

• Superelevation Rate

  Uncapped road-curve superelevation estimate e=v²/(gR)−f from speed, radius and assumed lateral friction; not a design-code limit.

• Escape Velocity

  Ideal two-body escape speed √(2μ/r) at a specified center-to-center radius; ignores atmosphere and rotation.

• Bernoulli Total Head

  Total ideal-flow head as elevation plus pressure head and velocity head; excludes friction and pump terms.