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Easy Centigrade-Fahrenheit and Kilos-Pounds Conversions

Sun, 2007–Nov–25

Traveling between cities in the US and other countries requires conversions between Centigrade and Fahrenheit, as well as between Kilos and Pounds. Here's a easy way to do the calculations, inspired by the faint childhood memories of the Trachtenberg method of arithmetic manipulations, and achieving error rates of 1% or less.

Converting Centigrade to Fahrenheit
DSA-32
DOUBLE, SUBTRACT one-tenth, ADD 32 		Converting Fahrenheit to Centigrade
32-SHA
SUBTRACT 32, HALVE, ADD one-tenth
The exact formula: °F = °C * 9/5 + 32
The easy formula is the same.

Easy conversion using D-S-A (or DSA-32) steps, with example converting 14 °C:
1. Double: 28
2. Subtract one-tenth: 28/10 = 2.8, rounded to 3, gives 28 - 3 = 25
Ignore negative sign if any, to make it easier, and then put sign back again.
3. Add 32: 25 + 32 = 57 °F [exact value is 57.2 °F]

 The exact formula: °C = (°F - 32) * 5/9
The easy but approximate formula: °C = (°F - 32) * 1/2 * 1.1

Easy conversion, using S-H-A (or 32-SHA) steps, with example converting 57 °C:
1. Subtract 32: 25
2. Halve: 12.5
3. Add one-tenth: 1.25, rounded to 1.3, gives 12.5 + 1.3 = 13.8 °C [exact value is 13.888... °C]
If no rounding is done, these steps provide the precise Fahrenheit value, with no error. This calculation leaves an error of around 1%; adding 1% to final result will give a more precise value in Centigrade.
The exact error is (5/9 - 1.1/2) / (1.1/2) = 1.0101...%, but 99% accuracy should be good enough for most day-to-day purposes.
Calculator:  °C →     °F (Exact & Easy)
  [Calculators Rounded to 1 Decimal Digit] 		Calculator:  °F →      °C (Exact) →     °C (Easy)

The Centigrade temperature scale is more properly called Celsius, but the term Centigrade continues to be in more common use in many countries.

Kilos and pounds are easier to convert, here are the examples:

Converting Kilos to Pounds Converting Pounds to Kilos
The exact formula: Pounds = Kilos * 2.2
The easy calculation formula is the same.

Example converting 72 Kilos:
1. Double: 144
2. Add one-tenth: 14.4, gives 144 + 14.4 = 158.4 [the exact value]

 The exact formula: Kilos = Pounds / 2.2
The easy but approximate formula: Kilos = Pounds/2 * 0.9

Example converting 160 Pounds:
1. Halve: 80
2. Subtract one-tenth: 8, gives 80 - 8 = 72 [exact value is 72.7272...]
If no rounding is done, this gives the precise value for Pounds. This calculation leaves an error of around 1%; adding 1% to final result will give a more precise value in Kilos. The exact error is (1/2.2 - 0.9/2) / (0.9/2) = 1.0101...%, but 99% accuracy should be good enough for most day-to-day purposes.
Calculator:  Kilos →     Pounds (Exact & Easy)
  [Calculators Rounded to 1 Decimal Digit] 		Calculator:  Pounds →     Kilos (Exact) →     Kilos (Easy)

Easier Method for Temperature - Divide or Multiply by 2?
As to whether the above method for Centigrade-Fahrenheit conversions is easy - well, it is easier than multiplying by 5 and dividing by 9. On the other hand, this is more complex than just dividing by 2, which is another way to handle 5 divided by 9, but that results in a greater error, one that is perceivable when experiencing the cold weather in Montréal!

For Fahrenheit to Centigrade conversions, using 1/2 instead of 5/9 gives an error of 11%, which can be a lot since 86 °F becomes 27 °C instead of the actual 30 °C.

For Centigrade to Fahrenheit conversions, using 2 instead of 9/5 gives an error that increases in proportion to the size of the Centigrade value, getting to a maximum of 20%. This can be a problem, for example, when looking at the thermostat that is set at 18 °C. Using the double and add 32 method gives 68 °F, but the correct value is 64.4 °F, and this difference will be noticeable in getting to the right level of warmth in the room.

Comments

Sat, 2012-07-14 11:27 — Anonymous (not verified)

Temperature/weight conversion methods

This type of thing drove me crackers for years. Even the 'easy' methods weren't that easy. I'm much happier with this. Thank you so much for a useful and informative website.