Calculate curb radius, arc length, and sagitta from chord and offset, or find offset from radius and chord in ft, in, mm, cm, or m.

Find radius from a chord and its midpoint offset.

Circular geometry only. A radius estimate does not establish a safe vehicle turning path or roadway design.

Perpendicular distance from the chord midpoint to the chosen arc.

Related Calculators

Curb Radius Formula

For a circular curb, a measured chord c and midpoint offset f determine the radius R:

R = (f) / (2) + (cยฒ) / (8f)

Variables:

  • R is the circular curb radius (length)
  • c is the straight chord joining the arc endpoints (length)
  • f is the perpendicular midpoint offset, or sagitta (length)
  • Use a consistent length unit. The calculator converts ft, in, mm, cm and m.

Calculate R = f/2 + cยฒ/(8f). Arc length is a = Rฮธ, with ฮธ in radians. For the minor arc, ฮธ = 2 asin(c/(2R)); a larger midpoint offset selects the major arc. The Arc + Offset mode numerically solves the circular-segment equations for a minor arc and requires a โ‰ฅ ฯ€f. See the circular-segment relationships.

What is a Curb Radius?

A curb radius is the curved edge of a roadway at an intersection or entrance to a roadway. It is designed to accommodate the turning path of vehicles, particularly larger ones like buses and trucks. Turning-path and pedestrian-safety design require vehicle geometry, site constraints and applicable engineering criteria. This calculator measures circular geometry and does not assess those design requirements.

How to Calculate Curb Radius?

The following steps outline how to calculate the curb radius:

  1. First, measure the straight chord between the circular arc endpoints.
  2. Next, measure the perpendicular offset from the chord midpoint to the arc.
  3. Choose the input and result length units.
  4. Use R = f/2 + cยฒ/(8f) to calculate the circular radius.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Chord c = 24 feet

Midpoint offset f = 2 feet

R = 2/2 + 24ยฒ/(8 ร— 2) = 37 feet