Free Surveying Tool
Spiral Curve Calculator
Enter a radius, spiral length, and intersection angle. Get TS, SC, CS, ST stations, tangent and external distances, throw, and a full spiral offset table — instantly.
Curve Parameters
Required
Radius of the central circular curve
Total deflection angle at the PI
Optional — for stations
Enter as decimal feet (e.g. 1000.00)
Spiral Curve Reference
TS
Tangent to Spiral — where the back tangent ends and the spiral curve begins.
SC
Spiral to Curve — where the spiral ends and the circular arc begins. Radius is constant from here through CS.
CS
Curve to Spiral — where the circular arc ends and the second (exiting) spiral begins.
ST
Spiral to Tangent — where the second spiral ends and the forward tangent begins.
p (Throw / Shift)
The offset of the circular curve from the original tangent line, created by inserting the spiral.
θs (Spiral Angle)
The angle subtended by the spiral, θs = Ls ÷ (2R). Doubled and subtracted from Δ to get the circular arc's central angle.
Key Formulas
θs = Ls / (2R)
p = Ls² / (24R)
k = Ls/2 − Ls³ / (240R²)
Ts = (R + p)·tan(Δ/2) + k
Es = (R + p)/cos(Δ/2) − R
Δc = Δ − 2θs, Lc = R·Δc
X(l) = l − l⁵/(40R²Ls²)
Y(l) = l³/(6RLs) − l⁷/(336R³Ls³)
Where l = distance along spiral from TS (ft), R = curve radius (ft), Δ = intersection angle
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