Surveying Formulas & 30 MCQ Test | MP Sub Engineer Civil

Surveying Formulas & 30 MCQ Test

Complete Surveying Formula Revision for Civil Engineering & MP Sub Engineer

📚 Surveying Formula Topics

Chain Surveying
Compass Surveying
Levelling
Theodolite Surveying
Tacheometry
Plane Table Surveying
Contouring
Curves
Area & Volume
30 MCQ Test

1. Chain Surveying Formulas

Basic relation:
Distance = Number of chain lengths × Chain length

Metric Chain:
20 m chain = 100 links
30 m chain = 150 links
1 link = 0.20 m

Area of Triangle:
A = ½ × b × h

Heron's Formula:
A = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2

Correction for incorrect chain length:
True length = Measured length × (Actual chain length / Standard chain length)

Correction for slope:
Horizontal distance = S cos θ

Difference in level:
h = S sin θ

Offset:
Perpendicular offset is normally used to locate details from a chain line.

2. Compass Surveying Formulas

Whole Circle Bearing (WCB):
Measured clockwise from North from 0° to 360°.

Reduced Bearing (RB):
Expressed from North or South towards East or West, between 0° and 90°.

Conversion:
N θ E → WCB = θ
S θ E → WCB = 180° − θ
S θ W → WCB = 180° + θ
N θ W → WCB = 360° − θ

Back Bearing:
If FB < 180° → BB = FB + 180°
If FB > 180° → BB = FB − 180°

Local Attraction:
Corrected bearing = Observed bearing ± Correction

Important: In absence of local attraction, the difference between fore bearing and back bearing is exactly 180°.

3. Levelling Formulas

Height of Instrument Method

HI = RL + BS

RL = HI − IS

RL = HI − FS

Rise and Fall Method

Rise = Previous staff reading − Current staff reading

Fall = Current staff reading − Previous staff reading

RL of next point = RL of previous point + Rise − Fall

Arithmetic Check:
ΣBS − ΣFS = Last RL − First RL

Alternative check:
ΣRise − ΣFall = Last RL − First RL

Curvature correction:
C_c = −0.0785 d² m

Refraction correction:
C_r ≈ +0.0112 d² m

Combined curvature and refraction correction:
C = −0.0673 d² m

d = distance in km.

4. Theodolite Surveying Formulas

Angle:
Horizontal angle = Difference between horizontal circle readings.

Vertical angle:
Measured with respect to horizontal line.

Deflection angle:
δ = 180° − Interior angle

Traverse:
Sum of interior angles = (n − 2) × 180°

Sum of exterior angles:
= 360°

Angular misclosure:
Observed sum − Theoretical sum

Average angle:
Mean angle = Sum of observations / Number of observations

5. Tacheometry Formulas

Stadia intercept:
s = Upper stadia reading − Lower stadia reading

Horizontal distance for inclined sight:
D = Ks cos²θ + C cosθ

Vertical difference:
V = (Ks sin 2θ)/2 + C sinθ

For anallactic lens:
C = 0

Therefore:
D = Ks cos²θ

For horizontal sight:
D = Ks + C

Common multiplying constant:
K = f/i

Common additive constant:
C = f + d

Here f = focal length, i = stadia hair interval and d = distance from instrument axis to objective.

6. Plane Table Surveying Formulas

Representative Fraction:
RF = Map distance / Ground distance

Scale:
Scale = 1 / RF denominator

Ground distance:
Ground distance = Map distance / RF

Map distance:
Map distance = Ground distance × RF

Important plane table methods: Radiation, Intersection, Traversing and Resection.

7. Contouring Formulas

Horizontal equivalent (HE):
HE = Horizontal distance between two consecutive contours

Vertical interval (VI):
VI = Difference in elevation between consecutive contours

Gradient:
Gradient = Vertical interval / Horizontal equivalent

Percentage gradient:
Gradient (%) = (Vertical difference / Horizontal distance) × 100

Slope angle:
tan θ = Vertical difference / Horizontal distance

8. Horizontal Curves Formulas

Simple Circular Curve

Tangent length:
T = R tan(Δ/2)

Length of curve:
L = πRΔ/180

Long chord:
LC = 2R sin(Δ/2)

External distance:
E = R[sec(Δ/2) − 1]

Middle ordinate:
M = R[1 − cos(Δ/2)]

Degree of curve:
D = 1718.9/R

Deflection angle for chord c:
δ = c/(2R) radians

Chainage of tangent point:
T₁ = Chainage of PI − T

Chainage of end point:
T₂ = T₁ + L

9. Area & Volume Formulas

Triangle:
A = ½bh

Rectangle:
A = l × b

Trapezoid:
A = ½(a+b)h

Circle:
A = πr²

Simpson's 1/3 Rule:
A = h/3 [y₀ + yₙ + 4Σy_odd + 2Σy_even]

Trapezoidal Rule:
A = h[(y₀+yₙ)/2 + Σy_middle]

Prismoidal Formula:
V = L/6 (A₁ + 4A_m + A₂)

Average End Area Method:
V = L/2 (A₁ + A₂)

⚡ Surveying Quick Revision Table

Topic	Important Formula
Back Bearing	BB = FB ± 180°
Height of Instrument	HI = RL + BS
Reduced Level	RL = HI − FS
Curvature	Cc = −0.0785d²
Combined correction	C = −0.0673d²
Simple Curve Tangent	T = R tan(Δ/2)
Curve Length	L = πRΔ/180
Long Chord	LC = 2R sin(Δ/2)
Stadia Distance	D = Ks cos²θ + C cosθ
Triangle Area	A = ½bh
Prismoidal Volume	V = L/6(A₁+4Aₘ+A₂)

❓ Frequently Asked Questions

Surveying में सबसे important formulas कौन से हैं?

MP Sub Engineer और Civil Engineering exams के लिए Levelling, Compass, Theodolite, Tacheometry और Curves के formulas विशेष रूप से important हैं।

क्या Surveying में numerical questions आते हैं?

हाँ। Bearing, RL, HI, curvature correction, tacheometry और simple circular curve से numerical questions पूछे जा सकते हैं।

Surveying की तैयारी कैसे करें?

पहले formulas याद करें, फिर हर formula पर 5–10 numerical questions solve करें और उसके बाद previous year MCQs की practice करें।

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Sunday, August 23, 2026