How this instrument works
The money multiplier is the textbook link between bank reserves and the deposits a banking system can support on top of them. It comes straight from a geometric series: a bank keeps back the reserve ratio r and lends the rest; the borrower deposits that loan elsewhere, and the next bank does the same thing with what's left. Sum every round of relending to infinity and the total collapses to a clean ratio, m = 1 ⁄ r — no calculus required, just the limit of a shrinking geometric sum.
The shape of the formula explains its behavior at the extremes. A 100% reserve requirement leaves nothing to relend, so m falls to exactly 1 — one dollar of reserves supports one dollar of deposits and nothing more. Push the ratio toward zero and m climbs without bound, because a bank that holds back almost nothing can relend almost everything, round after round. That blow-up is a feature of the model, not a market signal — it is the reason economics courses use this ratio to teach fractional-reserve mechanics rather than to forecast deposits directly.
Central-bank reserve requirements are set by policy, not by market rates, which is why this instrument treats the reserve ratio as a plain input rather than something the calculator derives. A macro student sanity-checking a textbook problem, a commentator explaining why quantitative easing didn't multiply the money supply as expected, or an analyst reconstructing a historical reserve regime can all read the ceiling this ratio implies without needing bank balance-sheet data.
- Enter the share banks must hold back into "Reserve requirement, %" — for example, 10 for a 10% requirement.
- Read "Money multiplier" — the instrument returns 100 divided by that percentage, the theoretical ceiling on deposit expansion.
- Lower the percentage to watch the multiplier climb, or raise it toward 100 to watch it collapse toward 1.
- Compare the result against published estimates of actual money-supply expansion, which sit well below this ceiling in practice.
Worked example — a 10% reserve requirement
Set "Reserve requirement, %" to 10. The instrument computes m = 100 ⁄ 10 = 10.0, the exact figure this page is built to reproduce. Picture it as a chain: a bank receives $1,000 in fresh reserves, keeps $100 back, and lends $900; that $900 is deposited elsewhere, that second bank keeps $90 and lends $810; and so on. Add the whole infinite chain and the deposits it creates sum to $10,000 — ten times the original $1,000, matching m = 10 exactly.
That figure is a ceiling, not a forecast. Real banks routinely hold reserves above the legal minimum, and not every dollar lent comes back as a fresh deposit — some sits as cash, some leaves the banking system entirely. Either leak shrinks the realized expansion below the textbook number. It is also worth noting that the reserve requirement itself is a policy dial: the United States held it at zero starting March 2020, which makes r undefined in the strict form of this formula and turns the ratio into a purely historical or comparative teaching tool for that period.
Questions
What does the money multiplier actually measure?
It measures the theoretical ceiling on deposit expansion implied by a single reserve requirement — how many total dollars of deposits one dollar of central-bank reserves could support if every bank lent out exactly the maximum allowed and every loan came back as a new deposit somewhere in the system. It is a modeling limit, not an observed quantity.
Why is the real-world multiplier usually lower than this number?
Because the formula assumes two things that rarely hold exactly: banks lend out every dollar above the reserve requirement, and every loan is redeposited rather than held as cash or sent abroad. Banks routinely carry excess reserves for liquidity and risk reasons, and some loan proceeds never return to a deposit account, so the realized expansion sits below the theoretical ceiling this instrument returns.
What happened to the U.S. reserve requirement?
The Federal Reserve set reserve requirement ratios to zero percent for all depository institutions starting March 26, 2020, removing the binding reserve constraint this formula describes. The ratio still has teaching and comparative value — for historical periods, other countries, or hypothetical policy scenarios — but it no longer reflects an active U.S. bank-reserve rule.
How does this differ from a bank's actual lending capacity?
This ratio describes a system-wide theoretical limit under simplified assumptions, not one bank's lending room today. Actual lending capacity depends on capital requirements, liquidity rules, deposit demand, and risk appetite — factors this instrument deliberately excludes so the reserve-ratio arithmetic stays visible on its own.
What happens as the reserve requirement approaches zero?
The multiplier grows without limit, since m = 100 ⁄ r and r is shrinking toward zero in the denominator. That is a property of the mathematical model, not evidence that near-zero reserve requirements produce unlimited real-world money creation — other constraints on bank lending take over long before the theoretical ceiling is reached.
Who typically works with this ratio?
Macroeconomics students checking a textbook problem, instructors illustrating fractional-reserve banking, and commentators explaining why a large reserve injection did not multiply the money supply as the simple formula would suggest. It shows up in explanatory writing about monetary policy more often than in a bank's own operating decisions.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.