---
title: "Stadia interval factor, additive constant"
subject: "Surveying II"
chapter: 2
key: "semester_4/surveying_ii:stadia-interval-factor-additive-constant"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/stadia-interval-factor-additive-constant
site: BCT Engineering
---

# Stadia interval factor, additive constant

Surveying II · Chapter 2: Tacheometry

- Asked in: 2074 Bhadra, 3 marks
- Video: [How to find the stadia interval factor K in stadia survey](https://www.youtube.com/watch?v=kiQWMcZoOIc) — Tutor Jack Ph
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/stadia-interval-factor-additive-constant
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2

## Question

What is stadia interval factor and additive constant? How these constants are determined?

## Short answer

Stadia interval factor K is f/i, usually 100; additive constant C is f+d, about 0.3 m external, zero for anallatic. Distance D=Ks+C. They are found by taking staff intercepts at known taped distances and solving K=(D2-D1)/(s2-s1), C=D1-Ks1.

## Answer

#### Stadia interval factor and additive constant
- **Stadia interval factor (multiplying constant) $K$:** the ratio $f/i$ of the focal length of the objective to the stadia hair interval. It is the number by which the staff intercept is multiplied to get the distance, usually 100.
- **Additive constant $C$:** the distance $(f+d)$ from the instrument's vertical axis to the objective's focus, in metres. About 0.3 m for an external focusing telescope, nearly zero for an internal focusing one, and exactly zero for an anallatic lens.

Distance: $D=Ks+C$.

#### Determination of the constants (field method)
1. On level ground, set up the instrument on a line and measure out several distances from it, say 50, 100, 150 and 200 m, with a tape. Mark with pegs.
2. Hold the staff vertical at each peg and read the stadia hairs. Compute the intercepts $s_1,s_2,\dots$ with the line of sight horizontal.
3. Write $D=Ks+C$ for two pegs and solve:

$$
K=\frac{D_2-D_1}{s_2-s_1},\qquad C=D_1-Ks_1
$$

4. Calculate $K$ and $C$ for several pairs and take the mean values, or fit by least squares from all readings.

Example: $D_1=50$ m, $s_1=0.497$ m; $D_2=150$ m, $s_2=1.497$ m give $K=100/1.000=100.0$, $C=50-49.7=0.30$ m.

## Check yourself

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

1. What is the stadia interval factor K?
   A. f/i, the ratio of focal length to stadia hair interval
   B. f + d
   C. i x f
   D. The staff intercept
   Answer: A. K = f/i is the multiplier giving distance from intercept, usually 100. (Key point: Stadia interval factor)

2. The additive constant C is
   A. f/i
   B. The distance (f + d) from the vertical axis to the focus; zero for an anallatic lens
   C. Always 100
   D. The staff intercept at 1 m
   Answer: B. C = f + d: about 0.3 m for external focusing, near zero for internal focusing, exactly zero for anallatic. (Key point: Additive constant)

3. How are K and C found in the field?
   A. Measure known distances, read intercepts with horizontal sight, solve D = Ks + C for two pegs
   B. Measure vertical angles only
   C. Compare bearings
   D. Use the subtense bar
   Answer: A. Two pegs give two equations in K and C. (Key point: Field determination)

4. Given D1, s1 and D2, s2, K equals
   A. (D2 - D1)/(s2 - s1)
   B. (D2 + D1)/(s2 + s1)
   C. (s2 - s1)/(D2 - D1)
   D. D1 s1
   Answer: A. Subtracting D = Ks + C for two pegs gives K = (D2 - D1)/(s2 - s1), then C = D1 - K s1. (Key point: Formula for K)

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