Gold-to-silver ratio: how to calculate and read it

The formula

Gold-to-silver ratio = gold price per troy ounce ÷ silver price per troy ounce

In Excel, =B2/C2, with both prices in the same currency and the same unit. A ratio of 80 means one ounce of gold costs as much as 80 ounces of silver. The ratio is the same in dollars, euros or grams, because the currency and unit cancel out.

Historical context

For centuries governments fixed the ratio by law, often around 15 or 16 to 1. Since the metals have floated freely, it has swung widely: it fell to roughly 17 in January 1980, when silver spiked, and rose above 120 in March 2020, when silver crashed at the start of the pandemic. Long-run averages depend heavily on the window: averages of about 60 since the 1970s and higher averages over the last twenty years are both quoted. Silver is also an industrial metal and much more volatile than gold, which is a big part of why the ratio moves so much.

Is the ratio high or low? Use a z-score

Some investors treat the ratio as mean-reverting: far above its average, silver looks cheap relative to gold, far below it gold looks cheap. A z-score measures "far" in standard deviations: =(D2-$D$13)/$D$14, with the average in D13 (=AVERAGE(D2:D11)) and the sample standard deviation in D14 (=STDEV.S(D2:D11)).

In the example the average is 81.2 and the standard deviation 7.7. Year 5, at 98.3, has a z-score of 2.23, the only year more than two standard deviations from the average. Year 6, at 71.1, is −1.31. A simple rule flags z above 1 as "silver cheap" and below −1 as "gold cheap" with a nested IF. The RSI and other indicators work on the same idea of comparing a value with its own history.

Worked example: ten years of the ratio and one switch

Year-end prices are inputs. The ratio, its average and z-scores are formulas, and the lower block runs the same ratio switch without and with dealer spreads.

Worked example: ten years of the ratio and one switch

	A	B	C	D	E
1	Year	Gold ($/oz)	Silver ($/oz)	Gold-to-silver ratio	z-score
2	Y1	1,260	17.50	72.0	-1.19
3	Y2	1,240	16.00	77.5	-0.48
4	Y3	1,290	15.90	81.1	0.00
5	Y4	1,410	16.60	84.9	0.49
6	Y5	1,690	17.20	98.3	2.23
7	Y6	1,820	25.60	71.1	-1.31
8	Y7	1,790	22.00	81.4	0.03
9	Y8	1,960	23.50	83.4	0.29
10	Y9	2,390	28.40	84.2	0.39
11	Y10	3,150	40.50	77.8	-0.44
12
13	Average ratio			81.2
14	Standard deviation (sample)			7.7
15
16	Ratio switch: gold → silver in Y5, back to gold in Y6			No costs	With spreads
17	Gold held before the switch (oz)			10.0	10.0
18	Spread: sell gold / buy silver (below / above spot)			1.0%	7.0%
19	Spread: sell silver / buy gold (below / above spot)			5.0%	3.0%
20	Silver received (oz)			982.6	909.1
21	Gold after switching back (oz)			13.82	11.79
22	Gain in gold ounces			3.82	1.79
23	Round-trip cost of the spreads				14.7%

Illustrative price series, not market data, and illustrative spreads. No dealer, mint or fund affiliation. Educational only, not investment advice.

The ratio switch, with and without costs

A ratio trader who holds 10 oz of gold sells it when the ratio is high and buys silver: 10 × 98.3 = 982.6 oz. When the ratio falls to 71.1, the silver buys back 982.6 ÷ 71.1 = 13.82 oz of gold, 3.82 oz more than before, without spending any new money.

Physical metal is not traded at spot, though. Selling gold 1% below spot, buying silver 7% above, selling the silver 5% below and buying gold 3% above costs 14.7% on the round trip, and the switch ends with 11.79 oz. More than half of the gain went to the spreads, mostly because silver coins and bars carry much higher premiums than gold. Storing about 98 times as much metal by weight is another cost the simple formula ignores. Use percent change to compare the result with simply holding gold.

What the ratio cannot tell you

Mean reversion is a tendency, not a law: the ratio can stay far from any average for years, and the average itself shifts with the window you choose. It also says nothing about whether gold and silver will rise or fall in price, only how they move against each other. Treat it as one input on relative value, not as a timing signal, and check current prices from a live source before acting on any number.

Common mistakes

• Dividing silver by gold. The ratio is gold ÷ silver. The inverse, about 0.012, answers a different question.
• Mixing units. Both prices must be per troy ounce (or both per gram) and in the same currency.
• Comparing with the wrong average. "High" against a 50-year average and "normal" against a 20-year average can both be true. State the window you use.
• Ignoring premiums and spreads. Physical silver often trades well above spot. A round trip can eat half or more of a ratio-switch gain.
• Treating mean reversion as a guarantee. The ratio can stay far from its average for years.
• Using STDEV.P on a short sample. For ten years of data use the sample standard deviation, STDEV.S.