---
title: "Degree of curve, elements of simple curve"
subject: "Surveying II"
chapter: 6
key: "semester_4/surveying_ii:degree-of-curve-elements-simple-curve"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/degree-of-curve-elements-simple-curve
site: BCT Engineering
---

# Degree of curve, elements of simple curve

Surveying II · Chapter 6: Curves

- Asked in: 2068 Bhadra, 7 marks
- Video: [Horizontal Curve Calcs   Circular Curve Elements   1](https://www.youtube.com/watch?v=jM6yeGSwccA) — Sandra Bowling
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/degree-of-curve-elements-simple-curve
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-6

## Question

What is degree of curve? Describe the elements of simple circular curve.

## Short answer

Degree of curve D is the angle subtended at the centre by a 30 m arc; radius R = 1718.87/D. Elements of simple circular curve: T = R tan(Δ/2), L = πRΔ/180, LC = 2R sin(Δ/2), E = R(sec(Δ/2)-1), M = R(1-cos(Δ/2)). PC chainage = IP - T, PT chainage = PC + L.

## Answer

#### Degree of curve
The degree of curve $D$ is the angle subtended at the centre by a standard arc (or chord) of fixed length $C$, usually 30 m in metric practice (100 ft in foot units). It expresses the sharpness of the curve: a bigger $D$ means a smaller radius.

$$
D = \frac{180^\circ\,C}{\pi R}\quad\Rightarrow\quad R = \frac{1718.87}{D}\ \ (C = 30\ \text{m})
$$

#### Elements of a simple circular curve
```text
              V (IP)
             /\
          T /  \ T
           / Δ  \
      T1  /      \  T2
       o'--------'o
         \ M  E /
          \ __ /
          R \  / R
             O
```

- **T₁ (PC)** and **T₂ (PT)**: the points where the curve begins and ends.
- **Deflection angle** $\Delta$: angle between the forward extension of the back tangent and the forward tangent; it equals the angle subtended at the centre by the curve.
- **Tangent length:** $T = R\tan(\Delta/2)$.
- **Length of curve:** $L = \pi R\Delta/180$.
- **Long chord:** $LC = 2R\sin(\Delta/2)$.
- **External (apex) distance:** $E = R(\sec(\Delta/2) - 1)$, from IP to the mid-point of the curve.
- **Mid-ordinate (versed sine):** $M = R(1 - \cos(\Delta/2))$, from the mid-point of the long chord to the mid-point of the curve.
- **Chainages:** T₁ = IP − $T$; T₂ = T₁ + $L$.

Example: $\Delta = 40^\circ$, $D = 4^\circ$ gives $R = 429.72$ m, $T = 156.40$ m and $L = 300.00$ m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does a larger degree of curve mean?
   A. A larger radius and flatter curve
   B. A longer tangent
   C. A smaller deflection angle
   D. A smaller radius and sharper curve
   Answer: D. R = 1718.87/D, so larger D gives smaller R and a sharper curve. (Key point: Degree of curve)

2. Degree of curve is the angle subtended at the centre by
   A. the whole curve
   B. a standard arc/chord of fixed length (30 m)
   C. the tangent length
   D. the long chord
   Answer: B. D is defined for a standard length, 30 m in metric practice. (Key point: Definition)

3. How is the deflection angle Delta defined?
   A. Angle between the forward extension of the back tangent and the forward tangent; equals the central angle
   B. Interior angle between the tangents
   C. Angle at T1
   D. Half the central angle
   Answer: A. Delta equals the angle at the centre, and the interior angle is 180 - Delta. (Key point: Deflection angle)

4. For Delta = 40 degrees and D = 4 degrees, R = 429.72 m. What is L?
   A. 429.72 m
   B. 300 m
   C. 150 m
   D. 156.4 m
   Answer: B. L = pi R Delta/180 = 300 m; equivalently 30 m x 40/4. (Key point: Example check)

## Related in Surveying II

- [Elements of simple circular curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-circular-curve-elements) — Surveying II, chapter 6
- [Degree of curve, elements of composite curve](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Adegree-of-curve-composite-elements) — Surveying II, chapter 6
- [Simple circular curve by deflection angle method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-deflection-angle-method-sketch) — Surveying II, chapter 6
- [Simple curve by offsets from long chord](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-offsets-long-chord) — Surveying II, chapter 6
- [Setting out simple curve by Rankine's method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asimple-curve-rankine-method-sketch) — Surveying II, chapter 6
- [Degree of curve, tangential angle formula](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Adegree-of-curve-tangential-angle-derivation) — Surveying II, chapter 6

## Related in other subjects

- [Simple circular curve elements and chainages](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-64s-simple-curve) — Transportation Engineering I, chapter 3
- [Composite curve with 48 degree deflection](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-72m-composite-60) — Transportation Engineering I, chapter 3
- [Car on circular curve, angular rate](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Acar-circular-curve-constant-speed) — Applied Mechanics (Dynamics), chapter 1