The Height Instrument HI Formula Auto Level is a key idea for surveyors and students. In this guide we explain the auto level, BS FS calculation method, and the reduced level booking method with clear numerical examples. The goal is to make learning simple and practical.
Basic Concepts and Terms
Below are short notes to help you understand the terms before we show calculations.
What is an Auto Level?
An auto level is an optical instrument used to find height differences. It makes leveling fast and accurate on construction sites and surveys.
What is Height of Instrument (HI)?
HI is the vertical height of the instrument line of sight above a reference bench mark or point. You use HI to get reduced levels.
Short Definitions: BS and FS
- BS (Back Sight) – a reading taken on a point of known reduced level, used to compute HI.
- FS (Fore Sight) – a reading taken on a point where you want the reduced level.
HI Formula and Calculation Method
Here we explain the mathematical steps and simple formulas. Read this small intro then see worked examples below.
Basic Formulas
Use these two simple formulas:
- HI = RL + BS
- RL = HI – FS
Step-by-Step Calculation Method
Follow these steps when you book reduced levels in the field.
- Start from a known bench mark (BM) with known RL.
- Take a BS on the BM and compute the HI.
- Take FS readings at new points and compute RL = HI – FS.
- If you need to move the instrument, use a change point (CP) or one of the new points as a BS to get the new HI.
Reduced Level Booking Method
This short intro explains how to record data in a level book. Use clear columns: Station, BS, FS, HI, RL.
How to Book Readings
Make a table or ledger with these columns. Write each setup separately. Always show how HI was found.
Common Booking Rules
- Write benchmark RL first.
- Show BS reading and compute HI immediately.
- Record each FS and compute RL below it.
- When you change setup, show the change point and new BS to find new HI.
Numerical Examples
We give two clear setups with numbers. This shows the HI formula and how BS FS calculations work in practice.
Example 1: Single Setup
Assume BM has RL = 100.000. Take BS on BM and two FS readings.
| Station | BS (m) | FS (m) | HI (m) | RL (m) |
| BM | 1.350 | 100.000 + 1.350 = 101.350 | 100.000 | |
| Point A | 2.125 | 101.350 | 101.350 – 2.125 = 99.225 | |
| Point B | 0.875 | 101.350 | 101.350 – 0.875 = 100.475 |
Notes: HI was computed once from BM. Then RLs for A and B are HI – FS.
Example 2: Changing the Instrument (Multiple Setups)
Continue from Example 1. Move the instrument and use Point B as a change point.
| Station | BS (m) | FS (m) | HI (m) | RL (m) |
| Point B (from prev) | 1.200 | 100.475 + 1.200 = 101.675 | 100.475 | |
| Point C | 2.325 | 101.675 | 101.675 – 2.325 = 99.350 | |
| Point D | 0.650 | 101.675 | 101.675 – 0.650 = 101.025 |
This shows how to transfer HI using a BS on the change point. The formulas remain the same.
Tips for Accurate Field Work
A few short tips to get better results when using an auto level and doing BS FS calculations.
- Keep the instrument stable and level before taking readings.
- Read the staff at eye level and avoid parallax.
- Always note the BM RL clearly.
- Use consistent units and round only at the end.
Common Errors and How to Avoid Them
Be aware of mistakes that affect the HI and reduced levels. Short list below.
- Using a wrong BM value — always double check.
- Missing a decimal or sign when recording readings.
- Forgetting to compute new HI after moving the instrument.
- Poor instrument setup causing sloping line of sight.
Frequently Asked Questions
What is the Height Instrument (HI) formula?
The HI formula is simple: HI = RL + BS. Once you have HI, find reduced level with RL = HI – FS.
How do you transfer HI when you move the instrument?
Use a change point or a point with known RL. Take a BS on that point, compute new HI = RL + BS, then take FS for new points.
What is the right way to book reduced levels?
Use columns for Station, BS, FS, HI, RL. Write BM first, then BS to get HI, then list FS and compute each RL. Show change points clearly.
Conclusion
Understanding the Height Instrument HI Formula Auto Level, the BS FS calculation method, and the reduced level booking method is simple with practice. Use the two formulas, record readings carefully, and follow the booking steps. The numerical examples above show how to apply the method in real surveys.
