Money Multiplier Calculator

Estimate how much new money the banking system can create from a reserve injection under fractional-reserve banking, using the standard deposit-expansion money multiplier formula.

Quick Facts

Formula
m = (1 + c) / (rr + er + c)
rr = required reserve ratio, er = excess reserve ratio, c = currency drain ratio.
Simple case
m = 1 / rr
With no excess reserves or currency drain, the multiplier is just the inverse of the reserve ratio.
Model
Fractional-reserve deposit expansion
A textbook ceiling on money creation, not a real-time measure of the money supply.

Your Results

Calculated
Money multiplier
-
m = (1 + c) / (rr + er + c)
Total money supply
-
Reserve injection × multiplier
New money created
-
Total money supply minus the initial injection
Total reserves held
-
Required plus excess reserves in the banking system

Ready

Enter the reserve injection, reserve ratio, excess reserve ratio, and currency drain ratio, then press Calculate.

How the Money Multiplier Calculator works

Under fractional-reserve banking, a bank that receives a new deposit or reserve injection is not required to hold onto all of it. It keeps a required fraction as reserves and lends out the rest; that loan typically ends up redeposited somewhere in the banking system, where the process repeats. Each round adds a smaller amount of new deposits than the last, and the sum of the whole chain is the money multiplier — the theoretical ceiling on how much the total money supply can grow from one unit of new reserves.

The formula

The full textbook money multiplier is:

m = (1 + c) / (rr + er + c)

where rr is the required reserve ratio set by the central bank, er is the excess reserve ratio (reserves banks hold voluntarily beyond the requirement), and c is the currency drain ratio (cash the public holds instead of redepositing it). The total money supply created is the reserve injection multiplied by m, and the money multiplier calculator uses this formula directly on your four inputs.

The simple case

When excess reserves and currency drain are both zero, the formula collapses to the version taught in introductory economics: m = 1 / rr. With a 10% required reserve ratio, m = 1 / 0.10 = 10, meaning a $10,000 reserve injection could theoretically support up to $100,000 of total deposits as it cycles through the banking system.

Worked example

Take a $10,000 reserve injection with a 10% required reserve ratio, no excess reserves, and no currency drain. The multiplier is 1 / 0.10 = 10, so the total money supply reaches $100,000 — the original $10,000 plus $90,000 of newly created deposits. Add a 5% currency drain (c = 0.05) and the multiplier falls to (1 + 0.05) / (0.10 + 0.05) ≈ 7.0, because some of each loan leaks out as cash instead of being redeposited and relent.

Why excess reserves and currency drain matter

  • Required reserve ratio: set by the central bank; a lower ratio allows more lending and a larger multiplier, a higher ratio restricts it.
  • Excess reserves: banks sometimes hold reserves beyond what is required, for liquidity or caution — every dollar held back is a dollar that does not get relent, shrinking the multiplier.
  • Currency drain: whenever a borrower or payee keeps cash instead of depositing it, that cash exits the deposit-and-relend cycle and reduces how far the reserve injection can multiply.

What this model does not capture

This is the classical, well-established theoretical multiplier used to teach fractional-reserve banking. It assumes every bank in the system applies the same ratios uniformly and that loan demand is unlimited. Real-world money creation also depends on how central banks actually implement policy, capital requirements, and how much banks and borrowers actually want to lend and borrow — so treat the result as an upper-bound estimate, not a forecast of the actual money supply.

Frequently Asked Questions

What is the money multiplier formula?
The full money multiplier is m = (1 + c) / (rr + er + c), where rr is the required reserve ratio, er is the excess reserve ratio banks hold voluntarily, and c is the currency drain ratio (cash the public holds instead of redepositing). The resulting money supply is the reserve injection multiplied by m. When er and c are both zero, the formula reduces to the simple textbook version, m = 1 / rr.
Why is the simple multiplier 1 divided by the reserve ratio?
In the simplest fractional-reserve model, every dollar deposited is lent out except the required reserve, and every dollar lent is redeposited and lent again. Summing that geometric process (1 + (1-rr) + (1-rr)^2 + ...) gives exactly 1 / rr, so a 10% reserve requirement implies each dollar of new reserves can theoretically support up to $10 of deposits.
What do currency drain and excess reserves do to the multiplier?
Both shrink the multiplier below the simple 1/rr figure. Currency drain removes money from the deposit-and-relend cycle each time someone holds cash instead of redepositing it. Excess reserves do the same when banks choose to hold reserves beyond what regulation requires, often for liquidity or caution. Higher values of either factor mean less deposit expansion from the same reserve injection.
Is this a real-time picture of the money supply?
No. This is the textbook theoretical ceiling for deposit expansion, assuming uniform ratios across every bank and no other leakages. Actual central-bank operations, loan demand, capital requirements, and public behavior mean real-world money creation rarely reaches the full multiplier implied by the reserve ratio alone.

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