Horizontal Curve Calculator

Design and set out curves with confidence. Choose your method, then review every key parameter. Export results, share with crews, and reduce rework today.

Calculator Inputs
Pick a method, enter known values, then calculate.
Changes station base and speed equation.
Use the method that matches your data.
Only used for degree-based mode.
Enter in metres or feet.
Central angle between tangents.
Arc length along centerline.
Works with the selected definition.
Distance PI to PC (or PT).
Straight chord PC to PT.
Optional. Supports “10+000” format.
preview
Creates points from PC to PT.
Typical: 20 m or 50 ft.

Optional speed check
Estimate a basic minimum radius using speed, superelevation, and side friction.
Uses km/h.
Example: 6% or 0.06.
Example: 0.15 or 15%.
Tip: Use Radius + Delta for standard geometry. Use the setout table for deflection angles and offsets. Verify control and datum.

Example Data
Sample inputs and outputs for quick validation.
UnitsRΔTLLCEM
Metric 300 m 40° 109.19 m 209.44 m 205.21 m 19.25 m 18.09 m
Expected: T ≈ 109.19 m, L ≈ 209.44 m. Minor differences can occur from rounding.

Formula Used
Core circular-arc relationships used in construction layout.
  • T = R · tan(Δ/2) — tangent length from PI to PC or PT.
  • L = R · Δ (radians) — arc length; with degrees: L = π·R·Δ/180.
  • LC = 2·R·sin(Δ/2) — long chord from PC to PT.
  • E = R·(sec(Δ/2) − 1) — external distance to curve apex.
  • M = R·(1 − cos(Δ/2)) — middle ordinate at mid-curve.
  • Setout by arc interval s: φ = s/R, deflection = φ/2, chord = 2·R·sin(s/(2R)).
  • Speed check (optional): Metric Rmin = V² / (127·(e+f)), Imperial Rmin = V² / (15·(e+f)).
How to Use This Calculator
A simple workflow for office calculations and field setout.
  1. Select units that match your drawings and survey control.
  2. Choose a compute mode based on the values you know.
  3. Enter inputs carefully, then add an optional PI station.
  4. Enable the setout table and select a practical interval.
  5. Press Submit to generate geometry and stationing outputs.
  6. Download CSV for staking notes or PDF for sharing.
  7. Cross-check results with plans before field work starts.

Horizontal Curve Guidance
Practical notes for design checks, layout, and documentation.

1. Why horizontal curves matter on site

Horizontal curves connect tangents smoothly, controlling vehicle path, drainage flow lines, and right-of-way use. In roadwork, a small change in radius can shift curb returns, widening, and utility conflicts. For building sites, curves govern access drives and fire routes where swept path and clearances are critical.

2. Core geometry produced by this calculator

The calculator reports radius (R), central angle (Δ), tangent length (T), arc length (L), long chord (LC), external distance (E), and middle ordinate (M). These values define the curve footprint and allow quick checks against plan callouts. Output units follow the chosen system for consistent field notes.

3. Multiple input paths match real project data

Projects rarely provide the same knowns. Some drawings specify R and Δ, while others give degree of curve or a measured curve length. The available modes let you solve from Radius + Delta, Degree + Delta, Radius + Length, Tangent + Delta, or Long Chord + Delta. This reduces manual rearranging and transcription errors.

4. Stationing and control points you can stake

When a PI station is entered, the calculator derives PC and PT stations using the tangent length and arc length. That creates clear control points for layout: set hubs at PI for alignment, then establish PC for curve start and PT for curve end. Stations are formatted in common “plus” notation for crews.

5. Setout table for deflection-based staking

The setout table generates points from PC to PT at a chosen arc interval. For each point it reports arc distance, station, central angle, and deflection angle. Deflection angles are useful with a total station from the tangent, while X and Y offsets support coordinate-based layout and quick sanity checks during field verification.

6. Practical interval selection and rounding

Common construction intervals are 20 m for roadway centerlines and 50 ft for conventional surveying, but tighter curves may require shorter spacing. The calculator automatically adds a final sub-chord if the curve length is not an exact multiple of the interval. Keeping consistent rounding across field sheets helps avoid cumulative station drift.

7. Speed, superelevation, and basic radius screening

The optional speed check estimates a minimum radius using design speed, superelevation (e), and side friction (f). Enter e as a percent or decimal and f as a decimal or percent. The output flags whether the computed radius meets the basic screening value, supporting quick feasibility checks before deeper standards review.

8. Quality checks and deliverables for closeout

Before issuing stakes, verify Δ matches the plan intersection angle and confirm units and station bases. Cross-check T and L against any plan tables and ensure PC/PT stations fall within project limits. Export CSV for staking sheets and the PDF for submittals, enabling traceable geometry during inspections and as-built preparation.

FAQs
Quick answers for common curve layout questions.

1) What is the difference between Δ and deflection angle?

Δ is the total central angle of the curve between tangents. Deflection angle is the angle turned from the tangent to a chord or point on the curve, commonly taken as half the central angle to that point.

2) When should I use Degree of Curve mode?

Use it when plans specify degree of curve rather than radius. Select the correct definition (arc or chord, 100 ft or 30 m) to match the drawings, then enter Δ to compute radius and all other values.

3) Does the setout table use arc or chord spacing?

The table steps along the curve by arc interval. It also reports the corresponding chord for each step and provides X and Y offsets. If your practice requires chord increments, use the chord values as guidance.

4) What station format is supported?

You can enter stationing as a plain number or plus format such as 10+000. The calculator converts it internally to a continuous distance, then formats PC and PT back into plus notation using the selected unit system’s station base.

5) How accurate is the PDF export?

The PDF is a simple text report generated directly in the file, suitable for sharing and recordkeeping. For full staking data, the CSV export provides the complete setout table with numeric precision and station fields.

6) What values should I use for e and f?

Use values specified by your project or governing standards. Typical superelevation might range from 2% to 8%, and side friction depends on speed and surface. The calculator performs a screening check, not a full design approval.

7) Why do I see a “sub” point near PT?

If the curve length is not an exact multiple of the chosen interval, the remaining distance is added as a final sub-chord point. This keeps the table aligned with PT while maintaining consistent spacing for most points.

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