Field guide
A practical guide to reviewing the calculation
Understand the inputs, review the geometry, and retain the assumptions with the results.
Start with the pair you actually know
This horizontal curve calculator solves one constant-radius circular arc from three explicit combinations: radius and central angle, radius and arc length, or radius and long chord. Select the combination before entering the second value. The same number can describe very different geometry depending on that selection. A length of 90 is not a turn of 90 degrees, and a long chord of 90 is not an arc length of 90. Keep the source drawing open while choosing the inputs, then compare the named outputs with its curve schedule.
The tool is useful when a curve table needs a second arithmetic check or when a drawing supplies one length but your next calculation requires another. It does not choose a suitable radius for a vehicle, check stopping sight distance, establish property boundaries, or approve a road alignment. Those decisions require project information beyond the two supplied values. Here the goal is a traceable geometric calculation that can be saved with the original inputs.
Enter angles without guessing their notation
Choose decimal degrees, explicit degrees minutes seconds, or radians for the central angle. In decimal mode, 86.28 means eighty-six and twenty-eight hundredths degrees. To enter eighty-six degrees and twenty-eight minutes, choose DMS and type 86 28 0. Minutes and seconds must each be less than sixty. Radians are available for values already expressed in mathematical form; changing the selector reinterprets the entry instead of converting the visible text automatically.
The central angle describes the complete turn of the circular arc. It is not the deflection from the starting tangent to the endpoint chord. A coordinate azimuth is another quantity again: it locates a direction relative to north. This page needs no coordinate azimuth because rotating the whole curve on a plan does not change its radius or lengths. Use the companion staking page when the curve must be placed at a particular coordinate and orientation.
Keep all lengths in one unit
Select metres, feet, or US survey feet to label the calculation. Every entered length must already use that same unit. The selector does not rescale the radius or second value. If a schedule uses feet while your working drawing uses metres, convert the relevant source lengths before running this calculation and retain a record of the conversion. Angle values are independent of the length unit.
A practical review begins with radius: confirm it refers to the intended alignment rather than an offset curb or another concentric feature. Then confirm whether the second length follows the curve or connects its endpoints directly. A clean numerical result cannot resolve a mislabeled drawing dimension. Keeping the known mode and original entry in the downloaded report makes this kind of review easier for the next person.
Read the elements as different measurements
The result separates arc length L, long chord C, tangent length T, external distance E, and middle ordinate M. Arc length follows the circular path. The long chord joins its endpoints directly. Tangent length measures from a curve endpoint to the intersection of the two endpoint tangents. The external distance reaches from that intersection toward the arc midpoint. The middle ordinate reaches from the chord midpoint toward the arc midpoint. These are different lines, even when a diagram makes two of them appear similar.
The table shows a formula beside each calculated value. Its formulas use the central angle in radians where required. The preview normalizes the radius and places a right-turning arc at a north-facing start, so it communicates shape rather than a real site position. A straight chord and short tangent direction indicators help orient the view. Read the numeric table for dimensions; do not measure pixels from the drawing or treat the editorial photographs as engineering diagrams.
Check a published example and a simple benchmark
The sample button loads the WSDOT manual example with radius 500 feet and central angle 86 degrees 28 minutes. Its published tangent and arc lengths round to 470.08 feet and 754.56 feet. The calculator keeps more digits internally, so comparing values at the source's stated precision is the appropriate check. This is a published worked example, not a record of measurements made by this website.
For a separate mental check, enter radius 100 and angle 90 degrees. The tangent length should be 100, the arc about 157.079633, and the long chord about 141.421356. Increasing the angle while holding radius fixed should increase these lengths within the supported range. Switching to radius plus arc or radius plus chord with sufficient retained precision should reconstruct the original angle. Rounding the supplied length first can produce a slightly different reconstructed angle.
Understand the supported domain
The calculation accepts a positive radius and a central angle strictly between zero and 180 degrees. A supplied chord must be positive and shorter than the diameter. A supplied arc must be positive and shorter than a semicircle at that radius. An impossible combination produces a message instead of quietly clamping the input into a different curve. Decimal length entries are limited to twelve decimal places and magnitude one trillion.
Very shallow arcs can have a tiny middle ordinate. The implementation uses an equivalent sine-squared expression to reduce cancellation when evaluating that value. Trigonometric outputs still use floating-point arithmetic, and additional displayed digits do not prove field accuracy. Near a half circle, tangent and external distance grow rapidly; check the source geometry carefully if those outputs seem unexpectedly large. The excluded 180-degree endpoint cannot have a finite tangent intersection of the type used here.
Save enough information for another review
Download the calculation CSV for a compact element list with units, or JSON for the original inputs, output values, timestamp, and software version. The report retains computational values rather than rounding all fields to the screen presentation. A colleague can therefore reproduce the calculation without transcribing numbers from an image. Save the report alongside the drawing revision that supplied the radius and second parameter.
Changing an input hides the previous result. Calculate again after changing the mode, unit, angle format, or number; this prevents an old table from being mistaken for the new scenario. Restore last inputs returns the last successful calculation's entries, while clear session removes the current entries and result. All calculation happens locally in the browser. The page does not send your entered geometry to a surveying server.
Move from elements to coordinates
When the elements are accepted, use the curve staking calculator to supply a starting easting and northing, forward tangent azimuth, turn direction, starting station, and arc interval. Those additional inputs determine where the curve lies and which points are generated. A radius and angle alone cannot provide site coordinates. Keep the same unit and original, unrounded geometry when moving between calculations.
This page excludes transition spirals, compound or reverse curves, vertical profiles, station equations, and geodetic arcs. Breaking a more complex alignment into unsupported approximations can change the intended shape. For a design containing those features, use a method that explicitly represents them. The simple-curve results here remain useful for checking the circular portions when their boundaries and parameters are independently known.