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Enter curve geometry and station interval to generate a field stakeout table.
Circular Curve Stakeout Visual
The calculator turns simple circular curve geometry into field-ready tangent, chord, and deflection notes.
What Is a Circular Curve Stakeout Calculator?
A circular curve stakeout calculator converts a simple circular curve into the field notes needed to set points along the curve. Instead of stopping at design elements, it builds the station-by-station layout table: PC, PT, arc distance from PC, sub-chord, long chord from PC, incremental deflection, and total deflection. This is the practical output a survey crew can use when turning angles and measuring chords with a total station.
How Tangent and Chord Stakeout Works
In tangent-and-chord layout, the instrument is commonly set at PC and referenced along the incoming tangent. Each curve point is reached by turning a deflection angle from the tangent and measuring a straight chord. Regular stations usually follow a chosen interval, while the first and last chords may be shorter when PC and PT do not fall exactly on interval stations.
Deflection Angle Formula for Circular Curves
The central angle to any point is based on arc length divided by radius. The field deflection to that point is one half of the central angle. The main formulas are:
L = pi * R * Delta / 180 C = 2R sin(Delta / 2) T = R tan(Delta / 2) deflection to point = central angle to point / 2 sub-chord = 2R sin(increment angle / 2)PC, PI, and PT Stationing
PC is the point of curvature, PI is the tangent intersection, and PT is the point of tangency. If the PC station is known, the calculator adds tangent length to get PI and curve length to get PT. If the PI station is known, it subtracts tangent length to find PC, then adds curve length to find PT.
Radius vs Degree of Curve
Some plans define a curve by radius, while older roadway and railway notes may use degree of curve. This tool supports direct radius, arc definition degree of curve, and chord definition degree of curve. Imperial degree calculations use the standard 100 ft base. Metric degree calculations use a 20 m base, which keeps the calculation suitable for metric stationing workflows.
Using the Stakeout Table in the Field
Use the station column to identify each layout point, the total deflection column as the angle turned from the PC tangent, and the long chord column as the distance from PC to that point. The sub-chord column is useful when setting consecutive points along the curve instead of always measuring from PC. Coordinate output is available when a PC coordinate and tangent azimuth are entered.
Limitations of Planar Curve Stakeout
This calculator assumes a local projected or construction coordinate plane. It is not a geodesic latitude/longitude curve solver. Final construction layout should follow the approved drawings, survey control notes, agency procedures, and any project-specific staking tolerances.
Related Surveying Calculators
- Horizontal Curve Calculator for design curve elements.
- Spiral Transition Curve Calculator for clothoid transition geometry.
- Superelevation Calculator for curve banking and runoff checks.
- COGO Point Calculator for point from bearing and distance.
- Line-Line Intersection Calculator for COGO intersections.
- Distance & Bearing Calculator for coordinate pair checks.
Frequently Asked Questions
What is the deflection angle in curve stakeout?
It is the angle turned from the tangent at PC to the chord that reaches a selected point on the curve. For a simple circular curve, it equals half the central angle to that point.
Does this replace roadway design software?
No. It is a field computation aid for simple circular curve stakeout. Design standards, agency requirements, and signed plans remain controlling.
Can I use latitude and longitude coordinates?
Use projected easting/northing or a local construction grid. Raw geographic coordinates are angular values and should not be used as planar stakeout coordinates.