From the reserve requirement ratio, compute the money multiplier: 1 ÷ reserve ratio, showing how much the banking system expands base money under fractional reserves.
Input Data
Results
At a glance:The money multiplier is the maximum amount the money supply can expand relative to the base money, equal to the inverse of the reserve ratio.
Formula
moneyMultiplier = 1 / (reserveRatioPct / 100)
$$m = \dfrac{1}{\text{Reserve Ratio}}$$How to Use
- Enter the deposit reserve requirement ratio.
- Read the resulting money multiplier.
FAQ
How does the money multiplier work, and how do banks 'create' money?
It comes from fractional-reserve banking. A bank keeps only a fraction of deposits as reserves and lends out the rest. That loan is spent and redeposited, becoming a new deposit the next bank lends out again — round after round, the same base money supports many times its value in deposits. With a 10% reserve ratio, HK$1,000 of base money can ultimately support about HK$10,000 of deposits; the 10× figure is the money multiplier. Banks do not print notes — they create deposits through the lending loop.
How does the reserve ratio affect the money supply, and how do central banks use it?
The reserve ratio and the money supply move in opposite directions, and the effect is amplified by the multiplier. Lowering the ratio means banks lend more, the multiplier rises, and the same base money supports more supply — an easing stance that stimulates the economy. Raising the ratio shrinks the multiplier and contracts supply — a tightening stance against overheating and inflation. Central banks also use other tools (open-market operations, policy rates), and some economies rely on rates more than reserve ratios, but the ratio → multiplier → supply chain remains the core framework.
Why is the actual money multiplier usually below the theoretical value?
This calculator gives the theoretical ceiling (1 ÷ reserve ratio), but reality is smaller because the model assumes banks lend every excess cent and all loans return as deposits. In practice, banks hold extra (excess) reserves for safety, especially in uncertain times, which does not re-enter lending. People also keep some cash in hand (a 'currency drain') that never flows back to banks to be re-lent. And if borrowers are reluctant to take loans, money is not created through the loop at all. A fuller formula is (1 + c) ÷ (reserve ratio + excess reserve ratio + c), where c is the cash-to-deposit ratio, so the observed multiplier is typically well below 1 ÷ ratio.
Is the money multiplier the same as the spending multiplier?
No. Both describe 'amplification', but in different domains. The money multiplier is about banking: it shows how base money (reserves) is expanded into broad money (deposits) via fractional reserves — 1 ÷ reserve ratio — answering 'how much deposit money does HK$1 of reserves create'. The spending multiplier is about output: it shows how autonomous spending (e.g. government spending) ripples through consumption into GDP — 1 ÷ (1 − MPC) — answering 'how much does HK$1 of spending add to GDP'. One is a monetary-policy mechanism, the other a fiscal/Keynesian one; they are not interchangeable.
What is the relationship between the money multiplier and base money / broad money?
The money multiplier connects the two layers of the money supply: base money (the monetary base, i.e. currency in circulation plus bank reserves, created by the central bank) and broad money (e.g. M2, the deposits everyone uses). In the simple model, broad money = base money × money multiplier. So with base money of HK$1,000 and a multiplier of 10, broad money is about HK$10,000. This is why a small change in base money can move the whole money supply by a larger amount when the multiplier is high — and why a falling multiplier (from more excess reserves or more cash holding) can blunt the effect of central-bank money injections. The figures here are theoretical ceilings; the actual ratio (M2 ÷ base money) is usually lower and shifts with bank behaviour and the economic cycle.
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.