# What is the rate?

Works out a rate as an amount per unit of time (rate = amount ÷ time), or the amount or the time from the other two, and converts the rate between seconds, minutes, hours, days, weeks, and years.

- Page: https://www.acalculator.org/math/rate-calculator
- JSON spec: https://www.acalculator.org/math/rate-calculator.json
- Version: b046248682da

## Default answer

Example with the default inputs (Amount 120, Time 2 h, Rate per hour): 120 in 2 h is a rate of 60 per hour.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| amount | Amount | How much was done, made, or travelled, in any unit: miles, pages, items, dollars. |
| time | Time | How long it took. |
| rate | Rate | The amount per time unit chosen below, such as 60 miles per hour. |
| per | Rate per | The time unit of the rate: per second, minute, hour, day, week, or year. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| amount | Amount | How much was done, made, or travelled, in any unit: miles, pages, items, dollars. |
| time | Time | How long it took. |
| rate | Rate | The amount per time unit chosen below, such as 60 miles per hour. |
| perSecond | Per second | The rate per second. |
| perMinute | Per minute | The rate per minute. |
| perHour | Per hour | The rate per hour. |
| perDay | Per day | The rate per day (24 hours). |
| perWeek | Per week | The rate per week (7 days). |
| perYear | Per year | The rate per year (365 days). |

## Method

Rate = Amount ÷ Time; Amount = Rate × Time; Time = Amount ÷ Rate, with the time counted in the rate’s time unit.

## Assumptions

- The rate is steady: the same amount in each unit of time.
- A day is 24 hours, a week 7 days, and a year 365 days.
- The amount and the rate are 0 or more, and the time is more than 0.

## Worked examples

1. amount = 120, time = 7,200, per = hour gives rate = 60, perMinute = 1, perDay = 1,440, perSecond = 0.016667. Source: Unit rates as in OpenStax Prealgebra 2e, section 5.6: https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate.
2. amount = 300, rate = 40, per = hour gives time = 27,000.
3. rate = 15, time = 5,400, per = minute gives amount = 1,350, perHour = 900.
4. amount = 52, time = 31,536,000, per = week gives rate = 0.99726, perYear = 52.

## FAQ

### How do I calculate a rate?

Divide the amount by the time: rate = amount ÷ time. 120 miles in 2 hours is 120 ÷ 2 = 60 miles per hour. The rate is in "amount per time unit", so keep the units: miles per hour, pages per minute, dollars per day.

### How do I find the amount from a rate?

Multiply the rate by the time: amount = rate × time. At 15 items per minute for 90 minutes, you make 15 × 90 = 1,350 items. Use the same time unit for both.

### How do I find the time from a rate?

Divide the amount by the rate: time = amount ÷ rate. 300 pages at 40 pages per hour take 300 ÷ 40 = 7.5 hours.

### What is a unit rate?

A rate for one unit of time (or of anything): 60 miles per 1 hour, or 1 page per 1.5 minutes. The calculator shows the unit rate for each of six time units at once.

### How do I convert a rate per hour to a rate per minute?

Divide by 60, because an hour has 60 minutes: 60 per hour is 1 per minute. To go from per hour to per day, multiply by 24: 60 per hour is 1,440 per day.

### Is this the same as speed?

Speed is one kind of rate: distance per time. This calculator works with any amount, so it covers speed too, but the speed calculator adds distance units such as miles and kilometers.

## Sources

- OpenStax, Prealgebra 2e, section 5.6 Ratios and Rate (rates and unit rates): https://openstax.org/books/prealgebra-2e/pages/5-6-ratios-and-rate
- NIST Special Publication 811 (2008), Appendix B.8, conversion factors (minute, hour, day, and year of 365 days to seconds): https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8