Money Multiplier Calculator
Enter a reserve ratio to find the money multiplier instantly. Choose between the simple model (1 divided by the reserve ratio) and the actual model that accounts for excess reserves and currency drain. The deposit expansion table shows exactly how each dollar of new reserves ripples through the banking system, round by round.
What is the money multiplier?
The money multiplier (also called the deposit multiplier or credit multiplier) measures how much the banking system can expand the money supply from a given amount of base money. When a bank receives a deposit, it keeps a fraction in reserve and lends the rest. The borrower spends that loan, which ends up as a deposit at another bank, which in turn keeps a fraction in reserve and lends the rest again. This chain of deposits and loans means the original dollar of reserves supports a multiple of that amount in total deposits. The simple money multiplier is the reciprocal of the reserve ratio: m = 1 / rr. A 10% reserve ratio yields a multiplier of 10, so $1,000 in new reserves can theoretically support $10,000 in deposits.
Simple model vs. actual model
The simple model assumes every dollar lent is immediately re-deposited in full. In reality, two leakages reduce the multiplier. First, banks voluntarily hold excess reserves above the regulatory minimum, often because loan demand is weak or because they prefer liquidity. Second, the public keeps some fraction of its money as cash rather than depositing it, which is called the currency drain ratio. The actual money multiplier accounts for both: m = (1 + c) / (rr + e + c), where rr is the required reserve ratio, e is the excess reserve ratio, and c is the currency drain ratio. Because the denominator is larger, the actual multiplier is always smaller than the simple one, which is why actual money creation is always below the theoretical maximum.
How to use this calculator
Select Simple for a quick result using only the reserve ratio, or Actual to include excess reserves and currency drain. Enter the required reserve ratio as a percentage (for example, 10 for 10%). In the actual model, also enter the excess reserve ratio and the currency drain ratio. Set the initial deposit to the amount of new base money entering the system. The calculator returns the money multiplier, total deposits generated, new money created, and a breakdown of where reserves and cash end up. The deposit expansion table shows every round of the lending cycle, from the first deposit through to convergence.
Reserve requirements and modern central banking
In the United States, the Federal Reserve reduced reserve requirements to zero in March 2020. The European Central Bank maintains a 1% minimum reserve requirement. Many other central banks have moved to frameworks based on interest rates rather than reserve ratios, making the textbook multiplier model a simplification of actual monetary policy. Despite this, the money multiplier remains a foundational concept for understanding how fractional reserve banking amplifies the monetary base into a larger money supply, and it is tested in economics courses worldwide. Use the actual model with a small required reserve ratio (and meaningful excess reserve and currency drain ratios) to model more realistic contemporary conditions.
Money multiplier by reserve ratio (simple model)
| Reserve ratio | Money multiplier | Lending fraction |
|---|---|---|
| 1% | 100.00 | 99% |
| 2% | 50.00 | 98% |
| 5% | 20.00 | 95% |
| 10% | 10.00 | 90% |
| 15% | 6.67 | 85% |
| 20% | 5.00 | 80% |
| 25% | 4.00 | 75% |
| 50% | 2.00 | 50% |
| 100% | 1.00 | 0% |
How the simple multiplier (1/rr) changes at common reserve ratios. Lower requirements allow greater deposit expansion.
Frequently asked questions
What is the money multiplier formula?
The simple money multiplier is m = 1 / rr, where rr is the required reserve ratio expressed as a decimal (so 10% becomes 0.10, giving a multiplier of 10). The actual money multiplier, which accounts for leakages, is m = (1 + c) / (rr + e + c), where e is the excess reserve ratio and c is the currency drain ratio. Both ratios are expressed as decimals.
Why is the actual multiplier smaller than the simple multiplier?
The simple model assumes all money remains in the banking system as deposits. In practice, banks hold extra reserves beyond the minimum (excess reserves) and the public keeps some money as cash rather than depositing it (currency drain). Both leakages remove money from the deposit creation cycle, shrinking the effective multiplier below its theoretical maximum.
What happens when the reserve ratio is zero?
Mathematically, a zero required reserve ratio makes the simple multiplier undefined (division by zero). In the actual model, if banks still hold excess reserves and the public still holds currency, the denominator stays positive and a finite multiplier still applies. In countries where reserve requirements have been abolished, the practical limit on deposit creation comes from bank capital requirements, loan demand, and central bank interest rate policy rather than a reserve ratio.
How does the deposit expansion table work?
The table traces each round of the lending cycle. In round 1, the initial deposit enters the banking system. The bank keeps a fraction as reserves and lends the rest. That lending becomes a deposit at another bank in round 2, which again keeps its reserve fraction and lends the remainder. This continues until the amounts become negligibly small. The cumulative deposits column shows the running total converging toward initial deposit times the money multiplier.
Does a higher money multiplier mean the economy is growing faster?
Not necessarily. A high multiplier shows the potential for credit expansion given the reserve structure, but actual money creation depends on banks being willing to lend and borrowers being willing to borrow. During recessions, banks may hold large excess reserves and loan demand may fall, so the actual expansion falls well short of the multiplier. The multiplier is a structural characteristic of the banking system, not a direct indicator of economic growth.
What is the currency drain ratio?
The currency drain ratio measures how much cash the public holds relative to the amount it keeps on deposit. If people deposit 95 cents of every dollar they receive and keep 5 cents as cash, the currency drain ratio is 5% (or 0.05 as a decimal). Higher currency drain means less money re-enters the banking system, which reduces how many additional deposits the system can create from a given amount of reserves.