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Reduced Level (RL): Methods to Calculate RL of a Point

Reduced level refers to equating elevations of survey points with reference to a commonly assumed datum. It is a vertical distance above or below the datum plane. The most common datum used is Mean Sea Level. This reduced level is the term used in levelling.

Reduced Level of a Point
Reduced Level of a Point

Methods to Calculate RL

The Reduced level can be calculated by two methods

  1. Height of instrument method

  2. Rise and fall method

Height of instrument method


It consists of finding the elevation of the plane of collimation i.e. (H.I.) for every setting of the instrument and then obtaining the reduced levels of the points with reference to the respective plan of collimation. This is done by

  • First, the H.L is calculated by adding the back sight of the R.L. of the starting point.

  • Then the reduced levels of the intermediate point and the first change point are obtained by subtracting the respective readings from the H.I.

  • When the instrument is shifted, a new plane of collimation is set up and the height of which is calculated by adding back sight reading to the R.L. of the first change point.

  • The reduced levels of the successive points and the second change point are found out by subtracting their staff readings from this new H.I.

  • This process is repeated until all the R.Ls are worked out, and then the arithmetical check is applied i.e. Σ B.S. – Σ F.S. = Last R.L. - First R.L.

Height of instrument Method
Height of instrument Method

Some more specifications about this method:

  • As it involves only a few calculations, there is a considerable saving of labour and time in the case of intermediate readings.

  • There is no check on the R.Ls of intermediate stations.

  • There are two checks for arithmetical accuracy i.e. the difference between the sum of back sights and sum of fore sights should be equal to the difference of the first and last R.Ls.

  • It is used for longitudinal and cross levelling operations.

Rise and fall method


In this method, the difference between consecutive points is calculated by comparing each point after the first with that immediately preceding it. The difference in their staff reading indicates a rise or fall according to as any staff reading is smaller or greater than that at the preceding point. The R.L. of each point is then found by adding rise or subtracting fall to or from the R.L. of the preceding point.

  • If B.S. - F.S. is positive then it is the rise

  • If B.S. - F.S. is negative then it is fall

  • R.L.= R.L. of previous point + (rise or fall)

  • To check Σ B S. – Σ F.S. = Σ Rise – Σ fall = (First R.L.) – (Last R.L.)

Specifications of this method are:

  • This method is slow and simple.

  • It is more precise because intermediate sight is also considered.

  • It is a laborious method as staff reading of each point on the ground after the first is compared with that preceding it, and the difference of level entered as a rise or fall.

  • There is a complete check on the reduction of R.Ls. of intermediate stations.

  • There are three checks for arithmetical accuracy. The difference between the sum of the back sights and the sum of the fore sights should be equal to that between the sum of rises and the sum of the falls as well as that between the first. and the last R.Ls.

  • It is used for earthwork calculations and other precise levelling operations.

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