How do you convert ounces to grams?

The factor looks measured. It is not. Since the 1959 international yard and pound agreement a pound has been exactly 453.59237 grams, and an ounce is a sixteenth of one:

1 pound  =  453.59237 g                          exactly
1 ounce  =  453.59237 ÷ 16 g   =  28.349523125 g   exactly
1 gram   =  1 ÷ 28.349523125 oz  =  0.035273961949580… oz

Dividing by 16 is dividing by 2 four times, and halving a decimal only adds places, so the ounce comes out to nine decimal places and then stops. The gram going the other way does not stop. As a fraction a gram is 1600000/45359237 of an ounce, and 45359237 is 7 × 11 × 97 × 6073, none of which a decimal system can divide out. Every grams to ounces figure you have ever read was rounded by somebody.

The two directions

Ounces to grams: multiply by 28.349523125. A quarter pound of butter:

4 × 28.349523125     =  113.3980925 g      →  113.4 g

Grams to ounces: divide by 28.349523125. A 250 g block of the same:

250 ÷ 28.349523125   =  8.818490487…  oz   →  8.82 oz

That first product is exact and the second quotient never ends, which is the whole asymmetry of this conversion in one pair of lines.

Why 4 oz is 113 g and not 100

Four is a round number and a hundred is a round number, and the eye wants them to be the same quarter pound. They are not close. A quarter pound is 453.59237 ÷ 4, which is 113.398 g, and 100 g is only 3.527 oz:

4 oz exactly     =  113.398 g
4 × 28           =  112 g       short by 1.4 g      (1.2%)
4 × 30           =  120 g       over by 6.6 g       (5.8%)
"call it 100 g"  =  3.527 oz    short by 13.4 g     (11.8%)

Rounding the factor to 28 costs 1.2%, and it costs that same 1.2% every time, because the error is in the factor and not in the amount: 8 oz comes out as 224 g against 226.8, and a full pound as 448 g against 453.6. For butter, flour and sugar that is inside the error of the scale. Rounding to 30 is a different proposition. 6 oz of chocolate becomes 180 g instead of 170.1, nearly 10 g over, and the recipe notices.

Swapping 100 g in for 4 oz is not a rounding at all. It is a 13.4 g cut, and the recipe will certainly notice that.

In your head: times 30, minus five and a half percent

Thirty is easy to multiply by, and 30 × 0.945 is 28.35, which matches the true factor to two thousandths of a percent. So multiply by 30, then take off 5.5% (half of ten percent, plus a tenth of that half):

4 oz   →  4 × 30  =  120   →  120 − 6.6   =  113.4 g      exact 113.398
8 oz   →  8 × 30  =  240   →  240 − 13.2  =  226.8 g      exact 226.796

If that is one step too many, multiply by 28 and accept being 1.2% light. Grams to ounces has two shortcuts of its own. Dividing by 28 runs 1.25% high. Multiplying by 7 and dividing by 200, which is multiplying by 0.035, runs 0.78% low:

250 g   →  250 ÷ 28         =  8.93 oz      exact 8.818    (1.25% high)
250 g   →  250 × 7 ÷ 200    =  8.75 oz      exact 8.818    (0.78% low)

Whichever you pick, round once, at the end. Rounding the factor and then rounding the answer stacks the two errors, and how many digits to keep is its own question, covered in how to round decimals.

Pounds and ounces to grams

Put everything in ounces first, then multiply. Going back, divide, and take out the sixteens:

1 lb 4 oz   =  16 + 4  =  20 oz   →  20 × 28.349523125   =  566.9904625 g

500 g       =  500 ÷ 28.349523125  =  17.637 oz  =  16 + 1.637    →  1 lb 1.6 oz
1 kg        =  1000 ÷ 28.349523125 =  35.274 oz  =  32 + 3.274    →  2 lb 3.3 oz

Past a few pounds the kilogram is the better unit, and the pounds and ounces machinery, with its 7.7 trap, is in how to convert kg to lbs. The short version is the same one as here: the decimal part of a pound is sixteenths, not tenths.

Three ounces, one word

The ounce in this article is the avoirdupois ounce, the one on a kitchen scale and a shipping label. It is 437.5 grains, and the grain is exactly 64.79891 mg, because a pound is 7000 of them. There are two other ounces, and a converter set to the wrong one will give you a confident wrong answer:

avoirdupois oz  =  437.5 grains  =  437.5 × 0.06479891 g  =  28.349523125 g
troy oz         =  480 grains    =  480 × 0.06479891 g    =  31.1034768 g
US fluid oz     =  29.5735295625 mL                        (a volume, not a weight)

The troy ounce is for gold, silver and the price of both. It is 9.7% heavier than the everyday ounce, so if a converter hands you 31.1 g for 1 oz, it is on the troy setting. The fluid ounce is not a weight at all. It is 29.5735295625 mL in the US, a different number in the UK, and how much it weighs depends on what is in it. A fluid ounce of water is about 29.6 g, since water is close to a gram per milliliter, and that is already 4% more than the 28.35 g weight ounce. Recipes that say "8 oz of milk" mean the fluid kind, which is a job for how to convert ml to oz, not this page.

Conversion table: ounces to grams

Every gram figure in the second column is exact. Multiplying ounces by 28.349523125 never produces more than ten decimal places:

Conversion table: grams to ounces

Where binary arithmetic slips

Ounces to grams is supposed to be the exact direction. Most whole numbers of ounces come through a floating point multiply unharmed: 4 × 28.349523125 is 113.3980925 on any machine. Then you weigh out 7 oz:

7 × 28.349523125   in binary floating point   =  198.44666187500002
7 × 28.349523125   exactly                    =  198.446661875

The stray 2 in the fourteenth decimal place is the same fault as 0.1 + 0.2 = 0.30000000000000004: 28.349523125 has no exact binary form, so the machine multiplies a number that is very slightly wrong. Prism stores the factor as the exact decimal it is, so 7 oz is 198.446661875 g, 11 oz is 311.844754375 g and not 311.84475437500004, and 0.1 + 0.2 is 0.3.

Or let the unit converter hold the 28.349523125

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