Curve Radius From Deflection Calculator

Work out curve radius from deflection instantly with clear inputs, formula shown and shareable results.

About Curve Radius From Deflection Calculator

Degree of curve is the central angle subtended by a standard length, usually 100 feet. On the arc definition the radius is 180 x basis / (pi x D), which gives the familiar 5729.58 divided by D for a 100 foot arc. The chord definition, used in railway practice, gives a slightly larger radius for the same degree.

Formulas

Arc definition

R = 180 x basis / (pi x D), giving R = 5729.58 / D for a 100 ft arc

Chord definition

R = (basis / 2) / sin(D / 2)

Worked example

With the default values below, Curve Radius From Deflection Calculator returns Curve radius of 1,145.9156. Change any input above and every figure here is recalculated in your browser.

Inputs used

Degree of curveaccepts 0.01–90 °: 5 °
Arc or chord basis lengthminimum 1 units: 100 units
Definition usedone of Arc definition, Chord definition: Arc definition

Results

Curve radius: 1,145.9156 units
Radius if the basis is in feet: 349.2751 m
Definition applied: Arc definition — radius from the arc subtending the degree of curve
Sharpness assessment: Moderate curve

Step by step

1Values used
2Arc definition
3Chord definition
4Curve radius= 1,145.9156 units
5Radius if the basis is in feet= 349.2751 m
6Definition applied= Arc definition — radius from the arc subtending the degree of curve
7Sharpness assessment= Moderate curve

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Curve Radius From Deflection figure worked out?

R = 180 x basis / (pi x D), giving R = 5729.58 / D for a 100 ft arc. Degree of curve is the central angle subtended by a standard length, usually 100 feet.

Why did degree of curve exist at all?

It made curve setting out possible with a chain and a transit: a one degree deflection per station meant the field party could lay out the curve without computing a radius.

What values do I need to enter?

This calculator takes 3 inputs: Degree of curve, Arc or chord basis length, Definition used. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.