Instrument I · The Ratio
The Ratio
Type a price for one bitcoin and a price for one troy ounce of gold, both in the same currency. The beam leans toward whichever costs more as a single unit, and the readout converts one into the other.
The balance and its inputs
The readout
Enter two prices to begin. The beam stays level until both are given.
- Troy ounces per bitcoin
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- Grams per bitcoin
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- The ratio
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- Bitcoin per troy ounce
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- Satoshis per troy ounce
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Your quantity: waiting for valid prices.
Beam angle: level, 0.0 degrees.
XAU side · Assumptions
What the numbers assume
Prices are whatever you type. The page never fetches a quote, so it cannot be out of date; only your numbers can. Take both prices from the same source and the same moment if you want the ratio to mean something.
Both prices must be in one currency. The currency menu changes the labels and nothing else. The troy ounce is 31.1034768 grams, not the everyday ounce of 28.349523125 grams, and mixing them up shifts every gram figure by roughly nine percent.
A quoted gold price is usually a reference for bullion of high purity. Coins, bars and jewellery trade with premiums, fees and storage costs that this calculator does not model. Neither does it model taxes, spreads or the cost of keeping a bitcoin safe.
BTC side · Method
How each figure is computed
- Troy ounces per bitcoin is the bitcoin price divided by the gold price per ounce.
- Grams per bitcoin is that figure multiplied by 31.1034768.
- The ratio is the same number written as ounces to one bitcoin. A ratio of 1 means the two unit prices are equal.
- Bitcoin per troy ounce is the gold price divided by the bitcoin price.
- Satoshis per troy ounce is 100,000,000 times that figure.
- Beam angle is 12 degrees times the hyperbolic tangent of 0.55 times the base-ten logarithm of the ratio.
The logarithm is there so that a ratio of ten and a ratio of a thousand both stay visible on a beam that can only tilt so far. The angle is a picture of the ratio, not a measure of anything else.
XAU side · Edge cases
When the input is awkward
Empty fields keep the beam level and say what is missing. Text, zero and negative numbers are refused with a plain message beside the field, and the readout stays blank rather than showing a broken figure. Prices below 0.000001 or above one trillion are declined, because arithmetic at those extremes tells you nothing useful.
If you convert more than 21,000,000 bitcoin, the page still does the arithmetic and adds a note: that is more than the rules allow to exist. Commas are read as thousands separators, so write decimals with a point. Your inputs are remembered on this device only, and the clear button forgets them.