Enter the principal and annual interest rate to estimate interest per hour (simple pro‑rata). For total interest accrued over a number of hours with a chosen compounding method, use the “Accrued Interest” tab.

Hourly Interest Calculator

Interest per Hour (Simple)
Accrued Interest

Enter any 2 values to calculate the missing variable (uses a 365‑day year = 8,760 hours)








Hourly Interest Formula

The following equations are commonly used to work with hourly interest.

H = \frac{P\cdot r}{8760}
I = P\left[\left(1+\frac{r}{8760}\right)^{t}-1\right]
  • Where H is the estimated interest per hour (currency/hour) using a simple pro‑rata of the annual rate
  • I is the total interest accrued over t hours (currency) assuming hourly compounding
  • P is the principal (initial amount of money)
  • r is the annual interest rate (in decimal form, e.g., 10% = 0.10)
  • t is the time in hours

If you want the interest per hour as a single constant estimate, use H = P·r/8760. If you want the total interest earned over a specific number of hours with hourly compounding, compute I by applying the hourly growth factor \((1 + r/8760)\) for t hours and subtracting the original principal.

What Is Hourly Interest?

Definition:

“Hourly interest” can refer to either (1) an estimated interest amount per hour based on an annual rate (often calculated as a simple pro‑rata amount), or (2) the total interest accrued over a number of hours when interest compounds on an hourly schedule. The calculator above supports both: the first tab estimates interest per hour, and the second tab computes total interest over a chosen number of hours under different compounding methods.

How to Calculate Hourly Interest?

Example Problem:

The following example outlines the steps and information needed to calculate the interest accrued over a given number of hours (with hourly compounding).

First, determine the principal. In this example, the principal is $5,000.

Next, determine the annual interest rate in decimal form. In this case, the annual interest rate is 10%, or 0.10.

Then, decide how many hours have passed. Let’s say 24 hours have elapsed.

Finally, calculate the total interest accrued over 24 hours using the formula above:

I = P × ((1 + r/8760) ^ t – 1)

I = $5,000 × ((1 + 0.10/8760) ^ 24 – 1)

Evaluating this gives I ≈ $1.37 of interest accrued over the 24-hour period (hourly compounding), so the balance would be approximately $5,001.37. (For comparison, the simple estimated interest per hour would be H = 5000×0.10/8760 ≈ $0.0571 per hour.)

FAQ

Does hourly interest make a big difference compared to daily interest?

Hourly compounding can slightly increase the total amount earned compared to daily compounding when both use the same nominal annual rate, because interest is credited more frequently. The difference is usually small over short periods, but it can grow over long time horizons or with higher balances and rates.

How do I handle different compounding methods?

For compounding n times per year over t hours (using a 365‑day year), you can use: A = P(1 + r/n)n·(t/8760), and then interest = A − P. For continuous compounding, use A = P·er·(t/8760).

Why divide by 8760?

There are 8,760 hours in a 365-day year (24 hours per day × 365 days). Dividing by 8,760 converts an annual rate to an hourly rate on that basis. Some applications use different day-count conventions (and leap years have 8,784 hours), so confirm which convention applies to your situation.