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Finance Calc Kit
Miscellaneous

Money Multiplier Calculator

Calculate macroeconomic simple money multiplier and total money supply expansion from bank reserve ratios and initial deposits.

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Simple money multiplier

10.00x

1 divided by 10.00% reserve ratio

Max money supply

$100,000.00

Potential total money created

Net credit created

$90,000.00

New lending capacity in the system

Required reserves

$1,000.00

Minimum reserves the bank must hold

Excess reserves

$9,000.00

Funds available to lend out

Money supply expansion

Max money supply$100,000.00
  • Initial deposit$10,000.0010.0%
  • Net credit created$90,000.0090.0%

How we calculated this

Open to see each step from your inputs to the result.

  1. 1. Convert reserve ratio to decimal

    RR=Reserve Ratio %100RR = \frac{\text{Reserve Ratio \%}}{100}

    RR = 10.00% / 100 = 0.10

  2. 2. Calculate the simple money multiplier

    M=1RRM = \frac{1}{RR}

    M = 1 / 0.10 = 10.00x

  3. 3. Estimate maximum money supply

    Max Money Supply=Initial Deposit×M\text{Max Money Supply} = \text{Initial Deposit} \times M

    Max Money Supply = $10,000.00 * 10.00 = $100,000.00

  4. 4. Calculate net credit created

    Net Credit Created=Max Money Supply−Initial Deposit\text{Net Credit Created} = \text{Max Money Supply} - \text{Initial Deposit}

    Net Credit Created = $100,000.00 - $10,000.00 = $90,000.00

  5. 5. Split the initial deposit into reserves

    Required Reserves=Deposit×RR,Excess Reserves=Deposit−Required Reserves\text{Required Reserves} = \text{Deposit} \times RR,\quad \text{Excess Reserves} = \text{Deposit} - \text{Required Reserves}

    Required Reserves = $10,000.00 * 0.10 = $1,000.00; Excess Reserves = $10,000.00 - $1,000.00 = $9,000.00

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What is the money multiplier?

The money multiplier estimates how much total money supply can expand from an initial bank deposit when banks lend out excess reserves and those funds are redeposited elsewhere in the banking system. Under a simple fractional reserve model, a 10% reserve requirement turns a $10,000 deposit into up to $100,000 of potential money supply. All calculations run in your browser.

The multiplier is a textbook macro concept, not a real-time Fed forecast. Actual money creation also depends on borrower demand, bank lending standards, and central bank policy. To model compounding growth from repeated reinvestment, use the compound interest calculator. To compare how output gaps influence interest rate policy, see the GDP gap calculator.

Money multiplier formulas

Convert the required reserve ratio from a percentage to a decimal, then divide one by that decimal:

M=1RRM = \frac{1}{RR}

Multiply the initial deposit by the multiplier to estimate maximum money supply, then subtract the original deposit to find net credit created:

Max Money Supply=Initial Deposit×M\text{Max Money Supply} = \text{Initial Deposit} \times M
Net Credit Created=Max Money Supply−Initial Deposit\text{Net Credit Created} = \text{Max Money Supply} - \text{Initial Deposit}

On the first bank's balance sheet, required reserves equal the deposit times the reserve ratio. Excess reserves are what remains available to lend:

Required Reserves=Deposit×RR\text{Required Reserves} = \text{Deposit} \times RR
Excess Reserves=Deposit−Required Reserves\text{Excess Reserves} = \text{Deposit} - \text{Required Reserves}

Worked example

Suppose a bank receives a $10,000 deposit and the required reserve ratio is 10%.

  • Reserve ratio decimal = 10% / 100 = 0.10
  • Money multiplier = 1 / 0.10 = 10x
  • Max money supply = $10,000 * 10 = $100,000
  • Net credit created = $100,000 - $10,000 = $90,000
  • Required reserves = $10,000 * 0.10 = $1,000
  • Excess reserves = $10,000 - $1,000 = $9,000

The first bank can lend $9,000. If that loan is spent and redeposited, the process repeats until reserve requirements absorb the expansion. The simple multiplier captures the upper bound of that chain.

Reserve ratio reference table

Reserve ratioMultiplier$10,000 deposit expands to
5%20x$200,000 max money supply
10%10x$100,000 max money supply
20%5x$50,000 max money supply
50%2x$20,000 max money supply

Simple model vs real banking

The textbook multiplier assumes every loan is redeposited, banks lend all excess reserves, and the public holds no cash outside banks. In practice, currency held by the public, voluntary excess reserves, and weak loan demand all reduce expansion. Central banks also influence reserves directly through open market operations and interest on reserve balances.

Frequently asked questions

What is the money multiplier formula?
The simple money multiplier equals 1 divided by the required reserve ratio expressed as a decimal. If the reserve ratio is 10%, the multiplier is 1 / 0.10 = 10.
How do you calculate maximum money supply from a deposit?
Multiply the initial deposit by the money multiplier. A $10,000 deposit with a 10x multiplier produces a theoretical maximum money supply of $100,000 under the simple fractional reserve model.
What is net credit created?
Net credit created equals maximum money supply minus the original deposit. For a $10,000 deposit expanding to $100,000, net credit created is $90,000.
What is the difference between required and excess reserves?
Required reserves are the minimum funds a bank must hold based on the reserve ratio. Excess reserves are the portion of the deposit above that minimum and represent funds available for new lending.
Does the Federal Reserve still use a 10% reserve requirement?
U.S. reserve requirements were simplified over time and many retail deposits currently have a 0% requirement, while larger institutions follow tiered rules. The 10% example remains the standard teaching case for how fractional reserve lending works.
Why is the actual money multiplier often lower than the formula?
People hold cash outside banks, banks may keep voluntary excess reserves, and loan demand varies. Those leakages mean real-world expansion is usually below the simple theoretical maximum.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.