Given a radius and a deflection, the whole curve falls out. Three relations do most of the work on a plan sheet.

Radius from degree of curve: $R = \dfrac{5729.578}{D}$. $R$ is the radius in feet, $D$ the degree of curve in degrees per 100 ft station. Sharper curve, bigger $D$, smaller $R$ — the two run opposite ways, always.

Tangent length: $T = R\tan\dfrac{\Delta}{2}$ — T equals R tan delta over two. $T$ is the distance from the PI back to the PC measured along the straight, $R$ the radius, $\Delta$ the deflection angle. The crew chains this one first, from the corner, to find where the curve starts.

Curve length: $L = \dfrac{100\,\Delta}{D}$. $L$ is the arc from PC to PT in feet. Read it as bookkeeping, not trigonometry: $D$ degrees are spent per station, $\Delta$ degrees must be spent in total, so $\Delta/D$ stations are needed, and each is 100 ft long.

Now the trap, and it is the one that costs money. The tangent takes half the deflection, not all of it. The curve is symmetric about the corner, so each straight sees only $\Delta/2$ of the turn. Using the full $\Delta$ sets the PC far too far back along the tangent — on a 60° bend it more than triples the distance — and the mistake does not announce itself until the curve fails to reach the PT.

Its quieter cousin: a calculator left in radians. Degrees are the field's unit and radians are the calculator's default, and $\tan 30$ is a perfectly finite number in both. Check the mode before the first tangent of the day.