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This article will discuss the Z axis of concreting, which we usually refer to as heights.

Concreting involves areaswhich are defined on the X and Y axis in 3 dimensional space. The Z axis is the third axis which gives us height, or depth.

Datum

For concreting purposes, a datum point or datum height is a point in space that has a known measured height. These heights are usually referred to as RLs which is short for reduced level.

Reduced Level

A reduced level (sometimes mistakenly referred to as a relative level) is a measurement of height used in construction or surveying usually based on the nearby average sea level.

Generally in construction we will call any measurement to do with height an RL or a height. (pronounced as the letter names: “ar el”)

Remember

RLs are written in metres.
Example: 5.450 to 4.000 indicates a difference of 1.450 metres, or 1450mm.

Rise and Fall

A change in height over a distance between two points is called a grade. A grade can be viewed as a rise or fall in height, depending on which way you are travelling along the run of the distance.

Example: if you walk 10 metres up a hill that is 1m higher at the top, you will rise 1m over 10m of run. This change in height is a difference of 10% or 1 in 10. (See article about Percentages)

If you were to walk down the same hill in the opposite direction, we would say the hill falls 1m over 10m of run.

Whether the difference in height is a “rise” or a “fall” is relative to the direction of travel.

In concreting, we usually call a difference in height a fall, because we are usually most concerned with where water is going to go when it ends up on the concrete, and water always travels down a hill.

Rise Over Run

The term rise over run is something you may have heard in high school math class. This part of math applies to concreting a lot.

As the example above showed, a change in height over a distance can be thought of as a rise or fall over some distance that we travel, or a run.

In construction, this is often said as either a value in percent or mm per metre. Let’s look at some examples of rise over run and how we can calculate these values.

Driveway

A driveway we need to lay is 25m long. From the garage, where the driveway starts, to the property boundary we know we have 1m of fall. From the boundary to the road is 3.5m. What is the fall in percentage, and in mm per metre?

Driveway Length = 25.0m
Road to Boundary = 3.5m
Subtract the distance from the road to the boundary, as our height point is at the boundary - not the road.
Garage to Boundary (Run) = 25.0m - 3.5m = 21.5m
Height difference from Garage to Boundary (Rise) = 1.0m
Therefore, the rise over run is: 1.0 / 21.5
= 0.046 or: 4.6%
How much rise in mm per metre?
Convert the Rise to mm: 1.0m = 1000mm
Then divide the Rise by the Run: 1000 / 21.5
= 46.51mm per metre
Every 1 metre that we travel along the driveway, we will rise 46.5mm. If we walk in the opposite direction, the driveway will fall 46.5mm every 1 metre.

Stairs

When building stairs rise over run is what it’s all about. The stairs are literally called risers (how high each step is) and runners (how long the top of each step is – also called the goings or treads)

We want to build a set of stairs in a backyard that will take us from a pathway at the bottom to a pathway at the top.
The height difference (Rise) between the two pathways will be 1.55m.
The distance (Run) we have to build the stairs in will be 3.0m.
If we want each riser to be 155mm, how many risers will we need to make and how long will each runner be?
1.55m = 1550mm (total Rise in height for complete set of stairs)
1550 / 155 = 10 (total number of Risers needed)
3.0m = 3000mm (total Run distance available for complete set of stairs)
3000 / 10 = 300mm (length of each Runner/going/tread)