COGO Survey

Horizontal curve calculator

Pick the two values you know. The rest of the circular curve is solved as you type, with a diagram drawn to shape.

Angles: degrees minutes seconds (24 30 15) or decimal degrees (24.5042).

Radius (R)
Delta angle (Δ)
Arc length (L)
Tangent (T)
Long chord (C)
External (E)
Middle ordinate (M)
Degree of curve (D, arc)

Curve formulas

With the delta angle Δ in radians and the radius R, every other part follows:

L = R × Δ arc length T = R × tan(Δ ÷ 2) tangent, PC to PI and PI to PT C = 2R × sin(Δ ÷ 2) long chord, PC to PT E = R × (1 ÷ cos(Δ ÷ 2) − 1) external, PI to the curve M = R × (1 − cos(Δ ÷ 2)) middle ordinate, chord to the curve D = 5729.578 ÷ R degree of curve, arc definition

When you know something other than R and Δ, the calculator first recovers them (for example Δ = 2 × atan(T ÷ R) from a radius and tangent) and then applies the formulas above.

Worked example

A curve has a 500 ft radius and a delta of 24°00′00″. Δ in radians is 0.418879, so L = 500 × 0.418879 = 209.440 ft. T = 500 × tan(12°) = 106.278 ft and C = 2 × 500 × sin(12°) = 207.912 ft. With the PI at station 12+50.00, the PC is at 12+50.00 − 106.28 = 11+43.72 and the PT is at 11+43.72 + 209.44 = 13+53.16.

What this page leaves to the app

  • PC and PT coordinates from a PI and two tangent directions.
  • A deflection-angle and chord stakeout table at any station interval.
  • Curve legs inside a traverse, with arc-aware area, plot and DXF export.

Questions

Which definition of degree of curve does this use?

The arc definition: the central angle subtended by a 100-unit arc, so D = 5729.578 ÷ R. It is the usual definition for highway work in feet. Railway work often uses the chord definition, which gives a slightly different radius for the same D.

What is the difference between the chord and the arc length?

The arc length (L) is measured along the curve from PC to PT. The long chord (C) is the straight line between the same two points, so it is always shorter. Deeds usually give both, along with the chord bearing.

Why does it reject a delta of 180° or more?

At 180° the two tangents are parallel and never meet, so the tangent and external distances have no finite value. Split a larger curve into two parts and solve each.

How are the PC and PT stations found?

PC station = PI station − T. PT station = PC station + L. Stationing runs along the curve, not along the tangents, which is why PT is not PI + T.

Is my data sent anywhere?

No. The calculation runs in your browser. Nothing you type leaves your device, and the page has no analytics or tracking.