# Tables 4: Common Conversions

Here are some of the more common conversions that are used in the building trades.

We also have a handy conversion calculator

To ConvertToMultiply By
kg (kilograms)lb (pounds)2.205
kPa (kilo Pascals)lbf/in² (pounds of force per square inch)0.1450
kPa (kilo Pascals)lbf/ft² (pounds of force per square foot)20.88
L (liters)gal (imperial gallons)0.2200
L/s (liters per second)gal/min (imperial gallons per minute)13.20
lx (lux)ft-candle0.09290
m (meters)ft (feet)3.281
m² (square meters)ft² (square feet)10.76
m³ (cubic meters)ft³ (cubic feet)35.31
mm (millimeters)in. (inches)0.03937
m³/h (cubic meters per hour)ft³/min (cubic feet per minute)0.5886
m/s (meters per second)ft/min (feet per minute)196.9
MJ (megajoules)BTU (British Thermal Units)947.8
N (Newtons)lbf (pounds of force)0.2248
RSI (insulation)R-value (insulation)5.6818

# Slope Conversion

There are two ways to measure a slope and each method of measurement can be converted to the other. The two ways are: ratio of rise to run or degree of angle.

Measurement One

Most carpenters are familiar with the ratio of the rise and run for stairs and rafters. The rise is vertical and the run is horizontal. A typical slope of the roof is 5:12, so the rise is 5" and the run is 12". Another way to look at this is the ratio of a slope when the rise is one compared to another value. 5:12, or 5 in 12, becomes 1:2.4 or 1 foot in 2.4 feet. Road builders refer to the gradient of a slope as a percentage. It is still a ratio but the rise is figured in 100 units of run. For example, a 10% gradient is 10 units of rise in 100 units of run, where the units are the same. 5 in 12 becomes 41.67% (percent which means per 100) or 41.67 feet rise in 100 feet or 41.67 inches in 100 inches or 41.67 metres in 100 metres. No matter what unit you use you must measure both the rise and run in the same unit.

Example: To calculate the slope of a roof (referred to as a pitch) of 5:12 to a percent of slope: Divide 5 by 12 = .4167, then multiply by 100 = 41.67%.

As a ratio to a rise of one: 5:12 becomes 1:2.4. (12 divided by 5 = 2.4). To convert 1:2.4 to a percentage, simply divide 1 by 2.4 = .4167, then multiply by 100 = 41.67% - the same as 5:12.

Measurement Two

The second way to measure a slope is by the angle of the slope (in degrees). If you know the angle of the slope you can convert that angle to a rise to run ratio.

This is done by using the tangent, which simply means the rise divided by the run at any given angle. The tangent of a known angle can be looked up in a table or by using a scientific calculator (a calculator that has a tangent button and usually lots of others). You can also find the angle of the slope if you know the rise to run ratio by using the inverse tangent on your calculator (the tangent in reverse, usually looks like this: tan-1) or by looking up the angle in a table of tangents where the angle corresponds to your known slope ratio. That's all a tangent is. It's just the ratio (fraction) of rise over run for any angle of slope.

One important note about angles in calculators. There are three ways to specify an angle (and you only need to know one of them unless you're an engineer): degrees, radians and gradians. You guessed it: degrees is the one to use. You can skip the other two and I won't bother you with their definitions!

The reason the above note is important is because you MUST set your calculator to degrees (instead of rads or grads) otherwise the results of your calculations will NOT be useful to you. There are many types and models of calculators. You want one that can calculate in degrees and has the tangent key (tan) and inverse tangent key (tan-1).

Using your Scientific Calculator to get the rise to run for any known angle of slope:

2. Tan 22.62 degrees = .4167. (On some calculators you need to enter the angle first, then press the tan key. On others you press the tan key first, then enter the angle.)
3. To convert this to a rise to run ratio multiply the answer by 12. So, in our example .4167 x 12 = 5. The rise to run is 5:12 (5 inches of rise for every 12 inches of run. A typical and useful slope for roofs.)

Using your Scientific Calculator to get the degrees of a slope from a known ratio of rise and run:

2. Divide rise by run. (Example: 5:12 or 1:2.4) 5/12 = .4167
3. Click the inverse tan button (tan-1). In our example, you will get 22.62 degrees as the result.
4. Or on some calculators you need to click the inverse tan button first, then enter .4167 to get 22.62 degrees as the result.

You can also check out our Conversion Calculator at our Construction Conversion Calculator and set the Convert field to Slope.

Dave

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