How the Money Supply Calculator works
This calculator applies the standard textbook money multiplier model from money-and-banking economics to show how a central bank's monetary base can expand into a larger total money supply through fractional-reserve banking. It is a deterministic model of the mechanics, not a live feed of official statistics.
The formula
The monetary base (MB), also called high-powered money, equals currency in circulation (C) plus the reserves banks hold (R). Reserves are the sum of required reserves (a fraction rr of deposits) and excess reserves (a fraction e of deposits) that banks choose to hold beyond the requirement. The public's preference for holding cash rather than deposits is captured by the currency-to-deposit ratio c = C / D. Combining these relationships and solving for deposits (D) gives:
D = MB / (rr + e + c), C = c × D, and total money supply M = C + D = MB × (1 + c) / (rr + e + c) = m × MB
The term m = (1 + c) / (rr + e + c) is the money multiplier: it tells you how many dollars of money supply each dollar of monetary base ultimately supports once banks finish re-lending deposits through the system.
Worked example
With a $1,000,000,000 monetary base, a 10% required reserve ratio, a 20% currency-to-deposit ratio, and a 1% excess reserves ratio, the denominator is 0.10 + 0.01 + 0.20 = 0.31, so the multiplier is (1 + 0.20) / 0.31 ≈ 3.87x. That produces roughly $3.87 billion in total money supply: about $3.23 billion in checkable deposits and $645 million in currency held by the public — and the two add back up to the total, since M = C + D by construction.
What moves the multiplier
- Required reserve ratio (rr): a higher requirement forces banks to hold back more of each deposit instead of lending it, so less new money is created and the multiplier falls.
- Excess reserves ratio (e): reserves banks hold voluntarily beyond the requirement — often to manage liquidity risk — sit idle rather than being lent out, which also shrinks the multiplier.
- Currency-to-deposit ratio (c): the more of the monetary base the public keeps as physical cash rather than depositing in banks, the less is available for banks to re-lend, so a higher c reduces the multiplier even though it also raises the numerator slightly.
Assumptions and limitations
This model assumes banks lend out every reservable dollar and that the currency and excess-reserve ratios stay fixed as deposits grow — a simplification of real bank behavior, which responds to credit demand, capital rules, and risk appetite. It also does not represent any single country's current regulatory regime: in the United States, for example, the Federal Reserve set statutory reserve requirement ratios to zero for all transaction accounts starting March 2020, so actual required-reserve inputs should reflect the rules in force where you are modeling. Use this calculator to understand the mechanics of deposit creation, not as a substitute for a central bank's published M1 or M2 money stock data.