How this calculator works
In a fractional-reserve banking system, each unit of central bank money can support several units of deposits. The monetary base is currency in circulation plus bank reserves, and the money supply here is currency plus checkable deposits. Their ratio is the money multiplier. When banks hold a larger fraction of deposits as reserves, or when the public holds more currency relative to deposits, the multiplier falls: fewer deposits can be supported by the same base. The often-quoted textbook figure 1 / reserve ratio assumes nobody holds currency and banks hold no excess reserves, so it overstates the real multiplier.
Formula
Money multiplier = money supply / monetary base, with money supply = currency + checkable deposits and monetary base = currency + reserves. Reserves = reserve ratio × deposits in the ratio mode, and the reserve ratio = reserves / deposits. In the known-multiplier mode, the implied base is money supply / multiplier and reserves are the base minus currency.
Worked example
With $2,000 of deposits, $100 of reserves and $200 of currency, the money supply is $2,200, the monetary base is $300 and the multiplier is 7.3333. The implied reserve ratio is 5%.
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Frequently asked questions
Why is the multiplier not simply 1 divided by the reserve ratio?
That shortcut assumes the public holds no currency and banks hold no excess reserves. Currency held by the public supports no deposits, and excess reserves do not multiply. Including both lowers the multiplier, which is why the observed ratio is used here.
Does a higher reserve ratio always shrink the money supply?
It lowers the multiplier for a given base. Central banks can offset this by expanding the base, and deposit flows can change deposits independently, so the money supply is not mechanically tied to the ratio alone.
Which deposits count?
This simple model uses checkable deposits, the part of the money supply banks create directly. Time deposits and money market funds belong to broader measures and are not created one for one by reserve balances.