Lessons · Engineering · SI and US units, and converting between them
Two systems of units, and carrying a number between them
A unit is part of the number. Converting is multiplying by a fraction that equals one, written so the old unit cancels.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
The pump datasheet is in gallons per minute, the pipe drawing is in millimetres and the site is in feet. The day a 12 in dimension is read as 12 mm is the day a bracket arrives that fits nothing, and it is the most common error in a first year.
How to think about it
Write the number with its unit, write the conversion factor as a fraction equal to one, and arrange the fraction so the unit you are leaving cancels on paper. Only then touch the calculator.
Worked example
1 in = 25.4 mm, exactlyThe one factor worth memorising. Everything between inches and millimetres comes from it.
3.5 in × (25.4 mm / 1 in) = 88.9 mmThe inches cancel top and bottom; millimetres are what is left. That is the whole method.
20 ft × (0.3048 m / 1 ft) = 6.096 mFeet to metres is the same shape. 0.3048 is also exact.
100 km/h = 100,000 m / 3600 s = 27.78 m/sTwo conversions in one line: kilometres to metres on top, hours to seconds underneath.
Your turn
Convert 8 ft to metres. Write the result.
8 ft × (0.3048 m / 1 ft) = m
Solve one, graded on the server
The trap
Multiplying when the fraction should be flipped. ft × (ft/m) leaves ft²/m, which is not a length. If the unit does not cancel on paper, the number is wrong however neat it looks.