Daily Periodic Rate Formula and Calculator

The daily periodic rate (DPR) is the interest rate applied to a balance for one day. Calculate it as the annual percentage rate (APR) divided by the number of days in the year used by the account: DPR = APR ÷ 365 for a 365-day basis, or APR ÷ 360 when the agreement specifies a 360-day basis. Enter the APR and day-count basis below to calculate the daily rate and its percentage equivalent.

Formula

The daily periodic rate is the annual percentage rate converted to a decimal and divided by the number of days in the applicable year:

Daily rate as a decimal: r_d = (APR ÷ 100) ÷ D
Daily rate as a percentage: DPR = APR ÷ D

• APR is the annual percentage rate, entered as a percentage per year.
• D is the day-count denominator used for the calculation: commonly 365 or 360; some methods account for a 366-day leap year.
• r_d is the daily rate as a decimal, with no unit.
• DPR is the daily rate expressed as a percentage per day.

The calculator displays the decimal rate and percentage rate separately because they are different numerical forms of the same rate. For example, 0.00049315 as a decimal equals 0.049315% per day. The rate is not a dollar amount; the balance and the method used to apply interest are also needed to calculate a charge.

Worked Example

Using the calculator’s default inputs—an APR of 18% and a 365-day basis:

1. Convert the APR to a decimal: 18 ÷ 100 = 0.18.
2. Divide by the day-count basis: 0.18 ÷ 365 = 0.0004931506849.
3. Express the same result as a percentage: 0.0004931506849 × 100 = 0.04931506849%.

Rounded to the calculator’s eight decimal places, the daily rate is 0.00049315 as a decimal, or 0.04931507% per day.

Assumptions

• The entered APR is treated as a nominal annual rate that is divided by the selected number of days; this calculation does not convert an effective annual yield into a daily rate.
• The selected denominator is used for every day in this simple rate conversion. A lender or account may apply a different day-count convention or adjust for a leap year.
• This calculator computes the rate only. It does not assume when payments or transactions post, how often interest compounds, or how a balance changes during the period.
• It does not include fees, taxes, insurance, or other account charges.

How a Daily Periodic Rate Works

A periodic rate is a rate assigned to a specific interval. A daily periodic rate describes one day, just as a monthly periodic rate describes one month. When an agreement calculates interest daily, it generally applies the daily rate to a balance for each day in the relevant period. The precise balance used, transaction timing, payment allocation, and rounding depend on the account’s stated calculation method.

As a simplified illustration, a constant balance of $1,000 multiplied by the example decimal rate gives $0.49315 of interest for one day before any rounding. That is only a one-day illustration, not a prediction of an actual statement charge: the balance may change, and the account’s terms determine how daily amounts accumulate and are posted.

Do not multiply a percentage directly by a dollar balance without converting it to a decimal. For a daily rate of 0.04931507%, use 0.0004931507 in a multiplication. Using 0.04931507 as the decimal would make the calculated amount 100 times too large.

Choosing the Day-Count Basis

The correct denominator is the one specified by the relevant agreement or calculation method, not necessarily the number of calendar days in the current year. A 365-day basis divides by 365, while a 360-day basis divides by 360. For the same APR, dividing by 360 produces a slightly larger daily rate than dividing by 365. A method may also use 366 days in a leap year or apply another convention.

For example, at an APR of 18%, the daily rate is 0.04931507% on a 365-day basis and 0.05% on a 360-day basis. The arithmetic difference does not establish which method applies to a particular account. Check the rate disclosure, contract, or statement for the stated basis. This calculator allows values from 360 through 366 so those common day-count choices can be entered.

Daily Rate Compared With APR and APY

APR is an annualized rate; the daily periodic rate is a per-day rate derived from it using a specified denominator. They are related, but they are not interchangeable. A daily rate alone does not tell you the total interest for a billing cycle unless you also know how many days are counted, what balance is used, and how the account treats payments and transactions.

APY, or annual percentage yield, reflects the effect of compounding over a year. Simply dividing an APY by 365 does not generally produce the same daily rate as dividing a nominal APR by 365. If you are given an effective annual yield and need a mathematically equivalent daily rate under daily compounding, the conversion is different: (1 + APY)^1/365 − 1, with APY expressed as a decimal. Use that only when the task is specifically to convert an effective annual yield and the 365-day compounding assumption fits.

Common Calculation Problems

• Mixing percent and decimal forms: Divide APR by 100 before using it as a decimal in a balance calculation.
• Assuming every account uses 365 days: Confirm whether the stated method uses 360, 365, 366, or another convention.
• Treating the rate as the interest charge: The rate must be applied to an eligible balance for the relevant number of days.
• Rounding too early: Keep sufficient precision during intermediate steps and round only as the account’s method requires. This calculator displays eight decimal places for the rate.
• Confusing a daily rate with monthly interest: A simple multiplication by the number of days is only an approximation when the balance is unchanged and the method is straightforward. Changing balances and compounding can affect the result.

Frequently Asked Questions

How do I calculate the daily periodic rate from APR?
Convert APR from a percentage to a decimal by dividing by 100, then divide by the applicable number of days. As a percentage per day, divide the APR percentage directly by that day count.

Is the daily periodic rate APR divided by 365?
It is when the applicable method uses a 365-day basis. Some agreements use a 360-day basis or another convention, so check the account terms rather than assuming.

How do I calculate one day of interest?
For a simple daily calculation, multiply the eligible balance by the daily rate in decimal form. For example, $1,000 × 0.0004931507 is about $0.49315 for one day, before account-specific rounding and adjustments.

Does the daily periodic rate include compounding?
No. The formula converts a nominal APR into a daily rate using a day-count denominator. How interest accrues or compounds over multiple days depends on the account’s method.

Is a daily periodic rate the same as APY?
No. APR is an annual rate, DPR is a per-day rate, and APY reflects annual growth including compounding. Dividing APY by 365 is not generally the correct conversion.

This result is an estimate for educational arithmetic; the lender’s disclosure gives the exact figures and calculation method.

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in apr | Annual percentage rate (APR) | % | 18 | 0.01 | 100
in days | Days in annual basis | days | 365 | 360 | 366
out dpr | Daily periodic rate | - | apr / 100 / days | 8
out pct | Daily rate as a percentage | % | dpr * 100 | 8