# Where does the 50.14348112 coefficent in the US Dollar Index formula come from?

The formula for the US Dollar Index (DXY) that every resource on the internet provides is: $$DXY = 50.14348112 × EURUSD^{-0.576} × USDJPY^{0.136} × GBPUSD^{-0.119} × USDCAD^{0.091} × USDSEK^{0.042} × USDCHF^{0.036}$$ Some also mention that DXY is the weighted geometrical mean of these exchange rates. So by calculating the weighted geometric mean in Excel I found that its actually the same as the above formula but without the 50.14348112 coefficent. So my question is where does it come from?

• The first coefficient in the formula (50.14348112) gives the value of the index to 100 on the date the reference began(1973 I think), when the main currencies began to be freely quoted relative to each other. Apr 9 '20 at 13:07
• Should have entered "50.14348112" in google Apr 9 '20 at 13:08
• You can make your comment an answer because it might be useful to others. Apr 9 '20 at 14:44

The US Dollar Index is the ratio of the US dollar (USD) to a geometric basket of six major foreign currencies – the Euro (EUR), the Japanese yen (JPY), the pound sterling (GBP), the Canadian dollar (CAD), the Swedish kroner (SEK) and the Swiss franc (CHF). The countries that use these currencies constitute the bulk of international trade with the United States, and also have well-developed foreign exchange markets, with rates freely determined by market participants.

The exponents that you write as superscripts come the constant weights of each component currency in the index:

EUR: 57.6%;

JPY 13.6%;

GBP: 11.9%;