Slope Converter

Why slope gets written three different ways on the same job

Slope is one of the few quantities in Australian civil engineering that is routinely expressed three different ways on the same set of drawings — as a ratio (1 in X), as a percentage (%), and as an angle in degrees (°) — and drafters are expected to move between them without thinking. A longitudinal road grade might be called up as 6%, the crossfall on the same carriageway as 1 in 40 (2.5%), a table drain batter as 1 in 6, and a cut batter in the geotechnical report as 34°. They all describe the same underlying idea — vertical rise divided by horizontal run — but the convention shifts by discipline. This converter exists so you can move between all four representations (ratio, percent, degrees, and rise/run) instantly while you are reading or checking a drawing, without opening a spreadsheet.

What "1 in X", "%", and degrees actually mean

The three formats are just different ways of writing rise over run:

• Ratio (1 in X) means one unit of vertical rise for every X units of horizontal run. 1 in 20 means 1 m up for every 20 m along. Smaller X = steeper.
• Percentage (%) is rise ÷ run × 100. So 1 in 20 = 5%.
• Degrees (°) is the angle the surface makes with horizontal, calculated as arctan(rise ÷ run). 1 in 20 works out to about 2.862°.

A common trap: percentage grade is not the same as the angle in degrees. A 100% grade is 45°, not 90° — because 100% means rise equals run (1 in 1). People who assume "100% = vertical" get slopes badly wrong. For the shallow grades civil work usually deals with (under about 10%), the percentage and the degree value happen to be numerically close, which lulls people into treating them as interchangeable — they are not, and the gap widens fast as slopes steepen.

Which convention is used where (Australian practice)

Handy conversion table

Worked examples

1. Reading a road grade. A design plan shows a 6% longitudinal grade over a 150 m chainage. That is 1 in 16.7, and it will fall 9.0 m over that length (150 × 0.06). If a reviewer asks "what's that in degrees?", it is about 3.43°.
2. Checking a pipe against a drainage table. A stormwater line is drawn at 1 in 150. Your drainage standard quotes minimum grades as a percentage — 1 in 150 is 0.667%, so you can compare it directly against the tabulated minimum.
3. Batter callout. A cut batter noted as 1 in 3 is 33.3%, or about 18.4°. If the geotech report gives a maximum stable angle in degrees, converting the drawn batter to degrees lets you check it in a single step.

Common mistakes

• Confusing 1 in X with X%. 1 in 20 is 5%, not 20%. The ratio and the percentage are inverses-of-sorts, and mixing them up is the single most common slope error on shop drawings.
• Assuming % equals degrees. Fine for very flat grades, wrong for anything steep (see 45° = 100% above).
• Dropping the direction. A converter gives magnitude only. On a real drawing, a +3% and a −3% grade meeting at a crest is a 6% change of grade — sign matters for vertical curves and driveway transitions.
• Rounding too early. Converting 1 in 20 to "2.9°" then back can drift. Keep the ratio or percent as the source value and treat degrees as derived.

Related standards and references

Slope conventions appear throughout Australian civil documents: Austroads Guide to Road Design (grades and crossfalls as %), the Queensland Urban Drainage Manual (QUDM) and council standard drawings (pipe grades as 1 in X), and AS 1428.1 for accessible ramp gradients. Angle-of-repose and batter stability values in degrees come from the project geotechnical report. This tool is a units converter only — always design to the figure and convention called up by the relevant standard and the local council.