Money multiplier and maximum deposit creation across reserve ratios
How the simple multiplier (1 ÷ reserve ratio) and the maximum new deposits it can support change as the required reserve ratio varies, holding your new reserves fixed. The row matching your reserve ratio is marked. These are theoretical ceilings under full lending and full redeposit, not amounts the banking system actually creates.
Reserve ratio
Money multiplier
Max deposit creation
2%
50.00
$50,000
5%
20.00
$20,000
8%
12.50
$12,500
10%
10.00
$10,000
◀ your ratio
12%
8.33
$8,333
15%
6.67
$6,667
20%
5.00
$5,000
25%
4.00
$4,000
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What it calculates: Money multiplier, Potential money creation.
A 10% reserve ratio lets each round lend out 90% of what it receives
A bank receiving 1,000 in deposits must hold 100 against a 10% requirement and can lend 900. That 900 is deposited somewhere, 90 is held and 810 lent, and so on. The series sums to 1/0.10 = 10, so 1,000 of new reserves can support 10,000 of deposits. The multiplier is simply the reciprocal of the reserve ratio.
Money Multiplier = 1 / Reserve Ratio; Max money created = Multiplier × New Reserves
The relationship is steep at low ratios. A 5% requirement gives a multiplier of 20; a 20% requirement gives 5. This is why reserve requirements were historically a policy lever — changing them changes how much money the banking system can create from the same base.
Cash held outside banks and excess reserves both break the chain
The model assumes every loan returns to the banking system as a deposit and every bank lends to its legal limit. Neither holds. Cash withdrawn and held outside banks leaves the circuit entirely, and banks routinely hold reserves well above the requirement — since 2008 they have held enormous excess reserves, which pays interest and carries no credit risk.
The observed money multiplier in most developed economies has therefore run far below the textbook figure, and in the period after 2008 the US ratio of broad money to base money fell below the theoretical minimum the requirement implied. A model producing 10 when the observed figure is nearer 3 is describing a mechanism, not a measurement.
Banks lend first and find reserves after, rather than waiting to be given them
The multiplier model implies causality running from reserves to lending: the central bank supplies reserves and banks expand credit on top. Most central banks now describe the relationship the other way — banks extend credit when they see profitable lending opportunities and creditworthy borrowers, creating deposits in the act, and then obtain whatever reserves settlement requires.
Under that description the binding constraints are capital requirements, loan demand and risk appetite rather than reserve ratios. Several major economies, including the US since 2020, have set reserve requirements to zero outright, which makes the textbook multiplier undefined and the mechanism it describes purely historical.
A teaching model, and an upper bound
This is the standard model in every introductory course and remains a clear illustration of how fractional reserve banking creates money from a base. Treat the output as the maximum the requirement permits under ideal assumptions, not as a forecast of what an injection will do.
For the amount of money actually in circulation, the monetary aggregates — M1, M2 and their equivalents — are measured directly rather than inferred from a multiplier. Comparing the implied figure here against the observed aggregate is itself a useful exercise in how far the model sits from the system it describes.
Frequently Asked Questions
What is the money multiplier?
The money multiplier is the ratio between the change in the money supply and the change in reserves that caused it. In the simple model it equals 1 divided by the required reserve ratio, showing how a small change in reserves can drive a larger change in deposits.
Why is the real-world multiplier usually smaller than the formula suggests?
Two leakages shrink it. Banks often keep excess reserves rather than lending every spare dollar, and the public withdraws some money as cash, which never re-enters the deposit chain. Both reduce how many lending rounds actually occur, so observed money creation falls short of the theoretical maximum.
What is the difference between required and excess reserves?
Required reserves are the minimum a bank must hold against its deposits, set by the reserve ratio. Excess reserves are anything held above that minimum. The simple multiplier assumes excess reserves are zero; when banks choose to hold them, the effective multiplier drops.
How does fractional reserve banking create money?
Under fractional reserve banking, a bank keeps only a fraction of deposits on hand and lends the rest. The borrowed money is spent and redeposited, becoming the basis for further loans. Repeated across the system, an initial deposit supports a much larger total of deposits, which is the money creation captured here.
Do modern central banks still rely on reserve requirements?
Several major central banks have cut reserve requirements to zero and instead steer short-term interest rates by paying interest on reserves. Where the requirement is zero, the simple reciprocal formula is undefined or meaningless, which is one reason the model is now taught mainly as an illustration.
What reserve ratio should I enter?
Use whatever ratio fits your scenario or coursework. A common textbook example is 10%, but you can model tighter or looser regimes by entering smaller or larger values to see how sensitively money creation responds.
Does a lower reserve ratio always mean more money creation?
In the simple model, yes: a smaller ratio raises the reciprocal and lifts the ceiling on deposits. In practice the effect depends on whether banks actually want to lend and whether borrowers want to borrow, so a lower requirement does not guarantee faster money growth.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Banks lend out every dollar of excess reserves and hold no voluntary buffer beyond the legal requirement.
All loaned funds are redeposited back into the banking system rather than held as cash outside it.
The required reserve ratio stays fixed throughout the chain of deposit creation.
Where it stops
The simple multiplier overstates real money creation because banks routinely hold excess reserves and borrowers withdraw cash, both of which leak out of the lending chain.
Many modern central banks operate with little or no reserve requirement, so the textbook reciprocal can be a poor guide to how money is actually created.
The model is a static ceiling, not a forecast; it ignores loan demand, credit risk, and the time it takes for deposits to circulate.
Related Calculators
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Velocity of MoneyHow many times each unit of money is spent in a year — nominal output divided by the money supply.
Inflation RateThe inflation rate between two CPI readings, with the index change alongside the percentage.
Average Propensity to ConsumeThe share of income spent and the share saved, from spending and income or from a consumption function.
Average Propensity to SaveThe saving rate as a share of disposable income, with the APC and the Harrod–Domar growth arithmetic.
Marginal Propensity to ConsumeThe share of an extra dollar that gets spent, from two observations, with the spending and tax multipliers.
Marginal Propensity to SaveThe share of an extra dollar saved — the leak that caps the multiplier — from two observations or the MPC.
Consumption FunctionConsumption, saving and the break-even income from C = a + bY, with the Keynesian-cross equilibrium.
Results are estimates for planning and analysis based on the figures you enter. They are not accounting, tax, or financial advice — verify with your own records and a qualified professional before making decisions.
Published the calculator with its formula, worked example, assumptions, limitations and a bespoke guide, and added an automated formula test suite covering it.
Verified that the multiplier is the reciprocal of the reserve ratio and that potential money creation scales linearly with the injection.
Frequently Asked Questions now show on the page: 7 answers, checked in a page-by-page audit.
What the calculation assumes and where it stops now show on the page.
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