How to find a level from backsight and foresight
A level instrument creates a horizontal line of sight. A staff reading tells you how far a point lies below that line. Start from a point with a known elevation.
What the formula is saying
Add backsight BS to known level RLA to find the line-of-sight elevation. Subtract foresight FS to find the new point level RLB.
Read the symbols in plain language
- RLA
- Known reduced levelm
- BS
- Backsightm
- FS
- Foresightm
Sort out the units first
All three inputs are in metres on the same vertical datum. BS and FS are staff readings, not horizontal sight distances.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- RLA · Known reduced level
- 100 m
- BS · Backsight
- 1.5 m
- FS · Foresight
- 0.8 m
Find the line-of-sight elevation
The staff reaches from the known point up to the horizontal sight line.
(100) + (1.5) = 101.5 mSubtract the reading at the new point
A larger staff reading means the point is lower below the same sight line.
(101.5)-(0.8) = 100.7 m
Does this worked answer make sense?
BS − FS = 0.7 m, so the new point is 0.7 m higher than the known 100 m point.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- RLA · Known reduced level
- 50 m
- BS · Backsight
- 1.2 m
- FS · Foresight
- 1.7 m
Find: a level from backsight and foresight
A hint, not the answer
Add backsight BS to known level RLA to find the line-of-sight elevation. Subtract foresight FS to find the new point level RLB.
All three inputs are in metres on the same vertical datum. BS and FS are staff readings, not horizontal sight distances.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the line-of-sight elevation
The staff reaches from the known point up to the horizontal sight line.
(50) + (1.2) = 51.2 mSubtract the reading at the new point
A larger staff reading means the point is lower below the same sight line.
(51.2)-(1.7) = 49.5 m
Avoid the common trap
Adding both readings is wrong: add backsight, subtract foresight. Do not confuse line-of-sight elevation with the tripod’s physical height.
When this method applies — and when it does not
One ideal instrument setup with upright staff readings. Real levelling also needs closure, observation and instrument checks; those are not performed here.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.