Rise and fall calculator
Reduce a rise and fall level book from backsight, intermediate and foresight readings. See reduced levels, arithmetic checks and closing misclose.
This tool runs in your browser and nothing you enter is uploaded. Check results independently before relying on them for survey work.
How it works
Between successive points, the previous reading minus the current reading gives a rise if positive, or a fall if negative. Add rises and subtract falls from the starting RL. At a change point the incoming FS sets the RL, then the new BS starts the next setup. The check compares ΣBS − ΣFS, ΣRise − ΣFall and last RL − first RL, using unrounded values and a 0.00000001 m arithmetic tolerance. A pass checks the calculation only, not the observations. Closing misclose is calculated last RL minus known closing RL; no adjustment is applied.
Worked example
Start RL 100.000 m. Book BS 1.500; IS 1.200; change point FS 1.000 and BS 2.000; final FS 1.800. RLs are 100.000, 100.300, 100.500 and 100.700 m. All three arithmetic differences equal +0.700 m. Against closing RL 100.695 m, misclose is +0.005 m.
Sources and further reading
For recommended equipment and procedures for differential levelling, including the equipment suggested for each level of misclose, see ICSM’s Guideline for Control Surveys by Differential Levelling, part of the Standard for the Australian Survey Control Network (SP1).
Frequently asked questions
How do I enter a change point?
Use one row for the point, with the old setup’s FS and the new setup’s BS. Leave IS empty. That row has one reduced level.
Does a passed arithmetic check prove the observations?
No. The check only compares the booking arithmetic. Reading, benchmark and transcription errors can still be present.
Is the closing misclose distributed?
No. The tool reports the difference against a known closing RL. It does not distribute corrections or apply a survey tolerance.
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