Money Multiplier Calculator (reserve ratio, cash & excess reserves)

Understanding the money multiplier calculator — concept and principle

The money multiplier links the monetary base created by a central bank with the broader money supply that results after banks lend and re-lend deposits. This calculator shows both the simple textbook multiplier and a more realistic one that allows for cash holdings and excess reserves.

Without leaks 1,000 of base money could support 10,000; cash holding and excess reserves cut that to 3,429.

How it is calculated

Simple multiplier: m = 1 ÷ rr, where rr is the required reserve ratio.
With leakages: m = (1 + c) ÷ (rr + e + c), where c = currency held by the public ÷ deposits and e = excess reserves ÷ deposits.
Change in money supply = m × change in the monetary base.
New deposits take the share 1 ÷ (1 + c) of the new money; currency takes c ÷ (1 + c).

The principle

When new reserves enter the banking system, a bank keeps a fraction and lends the rest. The borrower spends it, and it is deposited in another bank, which again keeps a fraction and lends the rest. Each round is smaller, and the total forms a geometric series whose sum is 1 ÷ rr times the original injection. In reality some money leaks out of the chain: people keep part as cash, and banks may hold more reserves than required. Those leakages enlarge the denominator and shrink the multiplier.

Worked example

Default inputs: reserve ratio 10%, currency ratio 20%, excess reserves 5%, new base 1,000.

Simple multiplier = 1 ÷ 0.10 = 10, so the simple change = 10,000.
Multiplier with leakages = 1.20 ÷ (0.10 + 0.05 + 0.20) = 1.20 ÷ 0.35 ≈ 3.429.
Change in money supply = 3.429 × 1,000 ≈ 3,429.
Deposits rise by 3,429 ÷ 1.2 ≈ 2,857; currency held by the public rises by 571.

Each point is the calculator re-run with only “Currency held by the public (% of deposits)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Currency held by the public (% of deposits)	Money multiplier (with leakages)
5	5.25
10	4.4
15	3.833
20	3.429
25	3.125
30	2.889
40	2.545

How to read the result

The leakage version shows why real-world multipliers are much smaller than textbook ones. Since March 2020 the US Federal Reserve has set reserve requirements at zero, and most modern central banks steer short-term interest rates rather than targeting the money supply. Treat the multiplier as a teaching model of how deposits are created, not a mechanical rule.

Common mistakes

Using the simple multiplier as a forecast of money growth.
Mixing up the currency ratio (cash ÷ deposits) with cash as a share of total money.
Entering percentages as whole numbers in the wrong field.
Assuming banks always lend out all excess reserves.

Keep in mind: This is a simplified textbook model. Actual money creation depends on loan demand, bank capital and central bank policy. Not financial advice.

Frequently asked questions

What is the money multiplier formula?

The simple version is 1 ÷ reserve ratio; with cash and excess reserves it is (1 + c) ÷ (rr + e + c).

Does the money multiplier still work with zero reserve requirements?

The simple version breaks down, but the leakage formula still describes the ratio of M1 to the base if c and e are stable.

Why is the actual multiplier lower?

People hold cash and banks keep excess reserves, so less of each deposit is lent on.

Sources: Mishkin, F. S., The Economics of Money, Banking and Financial Markets (money supply process) · Board of Governors of the Federal Reserve System, Reserve Requirements

Checked 9 Nov 2026. OpenStax, “Principles of Economics”, 3rd ed. (2022), section 27.4 “How Banks Create Money” (money multiplier 1 ÷ reserve requirement; cash holdings weaken it); Saylor Academy, “Money and Banking” v2.0, section 15.4 “A More Sophisticated Money Multiplier for M1” (m = (1 + C/D) ÷ (rr + ER/D + C/D)); Board of Governors of the Federal Reserve System, “Reserve Requirements” (0% from 26 March 2020).

Your numbers