Circular geometry · Local calculation

Curve Staking Calculator

Generate circular curve coordinates at arc-length intervals, review station and chord values, and export a two-dimensional point schedule.

Read the field guide ↓

Define the curve and generate points

Local processing · 0 < central angle < 180° · One constant radius

Decimal inputs: up to 12 decimal places and magnitude 10¹². Use spaces for DMS, e.g. 86 28 0; 86.28 means decimal degrees. No spirals, compound curves or latitude/longitude. Both endpoints are included; the final arc interval may be shorter. Up to 100,000 points.

From defined geometry to a reviewable result

Original contextual illustrations, not dimensioned survey evidence.

Plan the point sequence

Review the named inputs above, then use the guide to check what each output represents.

Survey pegs following an arc on compacted sand

Measure the right distance

Review the named inputs above, then use the guide to check what each output represents.

Measuring wheel beside curved chalk marks

Field guide

A practical guide to reviewing the calculation

Understand the inputs, review the geometry, and retain the assumptions with the results.

Place the geometry before generating points

This curve staking calculator turns a defined circular arc into a two-dimensional point schedule. Start with the beginning of the curve, its forward tangent direction, a constant radius, a turn direction, and one supported range definition. Then choose an arc-length interval and point numbering. The result includes the start, intermediate points, and end, together with station values, adjacent chord distances, tangent azimuths, and signed deflections from the starting tangent.

Use the preview to review a coordinate schedule before moving it into another application. This page does not connect to an instrument, establish control, transform a coordinate system, or measure as-staked positions. The starting coordinate and orientation must come from your own design and control information. A mathematically consistent table can still be in the wrong place if the chosen start is a tangent intersection rather than the actual beginning of the circular arc.

Identify PC and the forward tangent

Enter the easting and northing of PC, the point where the forward alignment leaves the straight tangent and begins the circular arc. The start is not PI, the intersection of the tangents. Set the tangent azimuth clockwise from coordinate north: north is zero degrees, east is ninety, south is one hundred eighty, and west is two hundred seventy. A backsight direction pointing away from the forward alignment must not be used as the forward tangent without resolving that reversal.

Choose decimal degrees or DMS explicitly for the tangent direction. This setting is independent of the central angle format. The central angle controls how much the curve turns; the tangent azimuth controls how the entire curve is oriented. For a quick orientation check, a north-facing start with radius 100 and a right turn through ninety degrees ends 100 units east and 100 units north of PC. Changing only the turn to left makes the easting displacement negative while keeping the northing displacement positive.

Select the range and length unit

The range can be defined by radius plus central angle, radius plus arc length, or radius plus long chord. The tool supports a single circular arc with a turn greater than zero and less than 180 degrees. It does not combine several arcs or add transition spirals. Radius and length entries must already use the same unit as the coordinates and stations. Selecting a unit labels the result; it does not convert previously typed numbers.

Record the design reference, coordinate system, and revision in the provided field. Confirm the start, direction, axis order, unit, and lack of generated elevation before calculation. This short context travels with the JSON report and makes assumptions visible during review. If your source calls northing X and easting Y, map those meanings to the named E and N inputs instead of copying the column order blindly. Geographic latitude and longitude are not supported by this planar calculation.

Space the points along the arc

The interval is measured along the curve from PC. It is not a straight distance between pegs, and it does not snap to a global full-station grid. For a start station of 808.15 and an interval of 50, the next scheduled station is 858.15. If the design instead requires full stations such as 850 and 900, this first version does not offer that scheduling mode. Do not reinterpret its output as an automatically aligned full-station table.

Both endpoints are included. When the full arc length is not divisible by the interval, the final point closes the remaining shorter arc segment. If the interval exceeds the entire arc, only the start and end are generated. Adjacent chord distance is reported separately for each point after the start, making the distinction between the scheduled arc increment and the direct point-to-point distance explicit. The first chord field is blank because no preceding generated point exists.

Keep station formatting separate from distance

Choose plain numeric stations, a two-digit suffix such as 10+50, or a three-digit suffix such as K1+050. The format applies to the entered start station and displayed output stations. It does not change the underlying accumulated distance or convert between feet and metres. The interval remains an ordinary positive length without a station plus sign. Negative start stations are accepted when their notation matches the selected format.

Display precision controls the station labels only. The report also contains unrounded station values and arc distances. With very small intervals and coarse labels, different points can have the same displayed station even though their underlying station values differ. Use the point identifier and unrounded values to distinguish those records, or increase display precision. Point numbering preserves leading zeros from the first number and adds your chosen prefix, creating an ordered set without recycling identifiers inside the generated table.

Review the endpoint and the shape

After calculation, the summary shows the number of points, turn direction, starting azimuth, endpoint coordinates, end station, and circle centre. Check those against an independent expectation before approving point export. The plot uses local coordinate differences from PC, with north up and east right at equal scale. This keeps the visible shape meaningful even when the absolute site coordinates are large. It is a plan view without a map background or elevation information.

The table is paginated, but exports include the complete generated schedule. The overview limits plotted markers for responsiveness; selecting a point with the keyboard includes that point in the view. The curve line samples the circular geometry independently of the chosen point interval, so two endpoint markers still appear on a curved path. For dense schedules, review the start, an interior point, the last regular interval, and the endpoint rather than assuming the first screen contains every record.

Export a schedule with clear coordinate meaning

Calculation CSV includes station, arc distance, previous chord, E, N, tangent azimuth, signed deflection, and unit. JSON includes the inputs, geometric elements, circle centre, complete point array, timestamp, and software version. These reports support review before point delivery. Approve the preview to enable a separate point CSV with Point, Easting, Northing, Elevation, and Description columns. The elevation field stays empty because this tool has no vertical design model.

Choose the matching column mapping when importing that point file into a checker, viewer, CAD package, or field controller. Some applications expect northing before easting or require a headerless file. Use an explicit conversion step for those requirements. Do not replace blank heights with zero unless zero is an independently specified design elevation. A separate grade calculation may supply heights, but matching stations, units, and vertical datum remains a distinct task.

Check assumptions and retain the calculation

The built-in example uses published WSDOT geometry, radius 500 feet and central angle 86 degrees 28 minutes, with a published rounded start station. Its origin, north-facing tangent, right turn, and interval are stated test assumptions. This demonstrates a reproducible computation without suggesting that the resulting coordinates are real survey control. A useful independent check is to inverse consecutive exported coordinates and compare their distances with the reported chords.

Calculations run locally in a worker and can be cancelled while preserving inputs. Editing any parameter invalidates the old result and disables point export until a new preview is approved. Restore last inputs helps recover the most recent successful scenario, while clear session removes it. Up to 100,000 points can be generated; CSV files are limited to ten mebibytes. Increase the interval if the requested schedule is too large. Floating-point trigonometry limits numerical precision, so stored decimal digits must not be treated as a guarantee of construction accuracy.

Frequently asked questions

Questions about inputs, geometry, and usable outputs.

How are circular curve coordinates generated?

The calculation places each arc-distance point in the local starting tangent frame, rotates it by the north-clockwise tangent azimuth, and adds the start coordinate. Turning left reverses the lateral component.

Is spacing based on arc length or chord length?

The requested interval is arc length from PC. The result separately gives the direct chord from the preceding generated point. A shorter final arc interval is included when needed to reach PT.

Does the tool start at PI or PC?

Enter PC, the beginning of the circular curve. PI is the tangent intersection and has different coordinates. This tool does not infer PC from a PI coordinate.

Why does changing left to right change the endpoint?

The turn determines which side of the forward tangent contains the circle centre. Mirroring that side mirrors the curve relative to the starting tangent, while preserving its element lengths.

Are full stations generated automatically?

No. Intervals are measured from the entered PC station. The page does not snap to a separate full-station grid or handle station equations.

Why is elevation blank in the point CSV?

Only horizontal geometry is defined here. An empty height preserves that absence. Add approved elevations in a separate workflow if your downstream application requires them.