Rates, speed, pace, fuel and transfer time

A rate is an amount of something per unit of something else: pounds per hour, kilometres per hour, litres per 100 km, megabits per second. This page covers writing rates, multiplying and dividing with them, and the special forms Varlig understands for running pace, fuel economy and download times. Reach for it when you’re working out pay for hours worked, how long a journey takes, a finish time for a race, what a trip costs in fuel or how long a file takes to download.

Rates build on ordinary units, so it helps to know the basics in Units and conversions. Prices per unit are covered in Money and currencies.

Rates with per and /

Write a rate with per or /. The two forms are identical. Multiply a rate by an amount of the unit underneath it and that unit cancels out, leaving a total:

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£12.50 per hour gives £12.50/hour

£12.50 per hour * 8 hours gives £100.00

£12.50/hour * 8 hours gives £100.00

£12.50/hour * 7h 30m gives £93.75

To convert a rate, name the whole target rate, such as £/month or m/s. Naming only the time unit (£36,000 per year in months) doesn’t work, because a month on its own isn’t a rate.

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£36,000/year in £/month gives £3,000.00/month

36 km/h in m/s gives 10 m/s

A rate doesn’t need a unit on top. A plain count per unit of time works for things like doses, visits or deliveries:

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2 per day gives 2/day

2 per day * 1 week gives 14

2 weeks at 3 per day gives 42

4 weeks at 37.5 hours/week gives 150 hours

30/week as /month gives 130.44375/month

A rate with nothing on top converts with a bare /month or /week as the target, so a weekly count reads as a monthly one.

Dividing an amount by a length of time gives the rate in the other direction, which is how you turn a spell of something into a daily or weekly figure:

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3 hours / 3 days gives 1 hour/day

3 hours / 3 days in hours/week gives 7 hour/week

How often something happens is a rate as well, so a dose, a class or a standing booking can be written the way you’d say it, with times a, once, twice or a word such as daily:

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3 times a day gives 3/day

twice a week * 4 weeks gives 8

take 2 tablets 3 times a day * 5 days gives 30

3 times a week at £5 gives £15.00/week

3 times a week at £6.50 * 4 weeks gives £78.00

£5 twice a week * 4 weeks gives £40.00

The price can go after at or in front, as in £5 twice a week, and multiplying by a length of time gives the total for that time. To see it over another period, convert it: 3 times a week at £6.50 in £/month is £84.79/month. 3 times 4 is still 12: times counts how often only when a period such as a day or weekly follows it.

A time in several parts can go in front of per too, and a small rate over grams or millilitres reads per kilogram or litre, the way labels and recipes quote it:

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2 hours 30 min per day gives 2 hours 30 min/day

20 min / 450 g gives 44.4444444444 min/kg

For elapsed time, Varlig counts a year as 365.2425 days and a month as 30.436875 days, the average lengths over the calendar. That means a rate over a year or a month rarely gives a whole number:

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3 per day for a year gives 1,095.7275

Periods in words

Write a price or an amount per period the way you’d say it: a or an before the period, per annum, per quarter, or a word such as weekly. It’s the same rate as one written with /:

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$25 an hour gives $25.00/hour

£5 a day gives £5.00/day

£45k per annum in £/month gives £3,750.00/month

£1,200 per quarter in £/year gives £4,800.00/year

£250 weekly gives £250.00/week

8 hours a day * 5 days gives 40 hours

The words are hourly, daily, weekly, fortnightly, monthly, quarterly, yearly and annually. A percentage joins a period the same way, so an interest or growth rate written 18% a year is 18%/year. a and an only mean “per” between an amount and a period, so is 2028 a leap year and a week from today keep their meaning. Money also takes the shorthand a listing or a payslip uses, such as £1,250 pcm or £45,000 pa; see Rent and pay shorthand.

Multiplying a rate by a plain number scales the rate, so £10.99 a month * 12 is still a monthly figure. When the number counts periods, as 12 months make a year, a hint on the line points this out: streaming * 12 shows “Still per month. For the yearly amount, write streaming per year.” Dividing works the same way, so $65,000 a year / 12 stays per year and suggests in $/month. For a year’s cost, convert it or say per year:

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streaming = £10.99 a month gives £10.99/month

streaming per year gives £131.88/year

streaming in £/year gives £131.88/year

Mixing amounts and rates

A bare amount and an amount per period don’t add up on their own, because the bare amount’s period is unknown. The error says what to write instead:

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£100 + £50/month gives Unsupported: an amount and an amount per month do not add up: write the amount per month too

£100/month + £50/month gives £150.00/month

Two rates over different periods do add up, because each one says what period it covers. The answer comes out in the period of the last rate, so write the period you want to read in last:

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£20/day + £300/week gives £440.00/week

£300/week + £20/day gives £62.86/day

In a budget worked out from names, though, the figures are already about the same period, so a plain amount beside money per month is read as a monthly figure:

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rent = £1,150 gives £1,150.00

insurance = £53.33/month gives £53.33/month

rent + insurance + £32 gives £1,235.33/month

The same goes for a year’s worth of a monthly cost written beside a yearly one, so you can compare two plans in one line:

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monthly plan = £12/month gives £12.00/month

annual plan = £120 gives £120.00

monthly plan * 12 - annual plan gives £24.00

A named amount of £10,000 or more given a shorter period is read as that amount each period, and the hint shows how to write a yearly figure instead:

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take home = £38,117.40 gives £38,117.40

take home per month gives £38,117.40/month

Weeks or days of a named amount need the amount’s period, since rent could be weekly or monthly:

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rent = £1,650 a month gives £1,650.00/month

5 weeks of rent gives £1,897.37

A distance or weight times a length of time needs its period too. 2,500 miles * 3 years asks you for the yearly figure:

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2,500 miles a year * 3 years gives 7,500 mi

Spreading a cost over a period

over spreads an amount across a period and gives you the rate. for keeps the amount as the price of the whole period, because that’s what £180 for 4 hours costs. Divide it by the period when you want the hourly figure:

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£1,980 over 10 months gives £198.00/month

venue = £180 for 4 hours gives £180.00

venue / 4 hours gives £45.00/hour

With a rate, for multiplies instead: 1.5 kW for 6 hours is 9 kWh, the energy a heater uses in that time, and 24 kW for 5 hours a day is 120 kWh/day.

Between two amounts of the same kind, over is their ratio, the way a rise over a run gives a gradient or a fall gives a pipe’s slope:

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60 mm over 3 m gives 0.02

48 m2 over 12 m2 gives 4

Pay and running costs

Converting a rate to a longer period counts every hour of the calendar, which suits a cost that runs all the time, such as a subscription or a fridge. For pay, multiply by the hours you actually work, or convert to a workday of eight hours:

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$25 an hour in $/year gives $219,145.50/year

$25/hour * 40 hours/week * 52 weeks gives $52,000.00

$25/hour in $/workday gives $200.00/workday

Turn it round with at to see how far a budget goes at a given price. Money at a price per unit gives you the units you can afford:

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£500 at £20/hour gives 25 hours

£1,200 at £45/day gives 26.6666666667 days

Days and hours in the same line count as working periods wherever they stand, so a week of eight-hour days prices up in one go:

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£20/hour * 5 days * 8 h gives £800.00

5 days * (8 h/day) gives 40 hours

Counting people and things

A price per person, or a count per day, multiplies by a count of the same thing, and the answer reads the way you’d say it:

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£12 per person * 6 people gives £72.00

£12 per person * 6 gives £72.00

£4.50 per coffee * 20 coffees gives £90.00

£4.80/unit * 250 units gives £1,200.00

£550/day * 22 workdays gives £12,100.00

8 glasses of water per day gives 8 glasses/day

8 glasses per day * 7 days gives 56 glasses

A plain number after a price per person counts people, as it does after any price per thing. Words that describe what you’re counting, such as of water, are left out of the answer. A meter reading or a day rate works the same way, so a bill or a month of contracting prices up in one line.

A name that counts a unit each period counts that unit whenever it meets the period, and a rate per that unit turns into a rate per the period:

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billable hours per week = 28 gives 28

billable hours per week * 46 weeks gives 1,288 hours

£65/hour * billable hours per week gives £1,820.00/week

8 hours per workday in hours per week gives 40 hours/week

A count @ a measurement is that many of it, which suits a cutting list:

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4 @ 910 mm gives 3,640 mm

cut list: 4 @ 910 mm + 3 @ 450 mm gives 4,990 mm

Two counts in a row multiply, so a quote can name who and for how long. A size written beside an x still measures each item rather than counting it, and a count per period at a price stays per that period:

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3 men 7 hrs @ £42/hr gives £882.00

3 people 2 nights at £60 gives £360.00

2 x 128 GB cards at £119 gives £238.00

6 hours a week at £13.20 gives £79.20/week

What each one holds can be a measurement rather than a price, a share of one thing said out loud is that share of what one costs, and containers of a size count the containers:

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14 boxes at 12 kg each gives 168 kg

9 at 1h 45m each gives 15 hours 45 min

half a bottle at £2.35 gives £1.18

60 bottles in cases of 12 gives 5 cases

6 items at £9.90 gives £59.40

items is an ordinary plural noun, so it needs no each of its own.

With nothing counted in front of it, every N units is a rate over that distance, and a price after it is what the thing costs you per mile or kilometre. That prices servicing, consumables and anything else you replace on a schedule:

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chain every 3,000 km at £34 gives £0.01133/km

service every 10,000 miles at £180 gives £0.018/mi

1 every 400 m gives 2.5/km

For packs, boxes and bullet-point shopping lists, see Shopping.

Speed, distance and time

Speed, distance and time follow the usual relationships. Multiply a speed by a time to get a distance, divide a distance by a speed to get a time, and divide a distance by a time to get a speed. rate for duration and duration at rate are other ways to write the multiplication.

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50 km/h * 2 hours gives 100 km

50 km/h * 2h 30m gives 125 km

70 mph for 2.5 hours gives 175 mi

2 hours at 65 mph gives 130 mi

120 km / 80 km/h gives 1.5 hours

250 km / 100 km/h in hours and minutes gives 2 hours 30 min

240 km / 3 hours gives 80 km/hour

10 km / 50 min in km/h gives 12 km/h

100 km/h in mph to 0 dp gives 62 mph

A journey time can be written in hours and minutes, as in 2h 30m, and the whole duration is used. Units also cancel when they’re written differently, so miles divided by miles per hour, or nautical miles divided by knots, gives a time straight away:

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300 miles / 60 mph gives 5 hours

250 miles / 60 mph in hours and minutes gives 4 hours 10 min

100 NM / 20 kn gives 5 hours

at works in both directions. A length of time at a speed is the distance covered, and an amount written in the rate’s own measure is how long that amount takes:

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100 km at 50 km/h gives 2 hours

67 miles at 50 mph gives 1.34 hours

40 hours at 4 hours a week gives 10 weeks

The last line is the one to reach for when you’re pacing work rather than a journey: forty hours of study at four hours a week takes ten weeks.

Pace

Runners and walkers usually think in pace, the time per kilometre or mile, rather than speed. Write a distance in a duration and Varlig shows the pace in minutes and seconds per unit of distance:

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5 km in 25 minutes gives 05:00/km

10 km in 55 minutes gives 05:30/km

3 miles in 27 minutes gives 09:00/mi

42.195 km in 3.5 hours gives 04:59/km

A pace of an hour or more per unit also shows hours, so 1 km in 60 minutes is 01:00:00/km.

Write the time the way your watch shows it: in one unit, in hours and minutes, or as a stopwatch time:

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5 km in 27 min 30 s gives 05:30/km

5 km in 26:45 gives 05:21/km

26.2 miles in 3 h 30 min gives 08:01/mi

42.195 km in 3:30:00 gives 04:59/km

400 m in 1:05 gives 02:43/km

A time with one colon is read the way a runner means it: 5 km in 26:45 took 26 minutes 45 seconds, while 42.195 km in 3:30 took three and a half hours. To be exact, write all three parts, as in 0:26:45. A pace over metres or yards is shown per kilometre or mile.

on does the same job as in, which is how interval sets get written down:

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100 m on 1:30 gives 15:00/km

400 m on 1:05 gives 02:43/km

You can also write a pace directly, as minutes and seconds per kilometre or mile, or as a time per distance:

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4:59/km gives 04:59/km

7:30/mi gives 07:30/mi

5 min 20 s per km gives 05:20/km

Finish times and distances from a pace

A pace calculates like any other rate. Multiply it by a distance, or write the distance at the pace, for a finish time. Divide a time by the pace for a distance:

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5:30/km * 42.195 km gives 3 hours 52 min 4.35 s

42.195 km at 5:30/km gives 3 hours 52 min 4.35 s

pace = 10 km in 55 minutes

pace * 21.1 km as laptime gives 01:56:03

1 hour / 5:00/km gives 12 km

6 min/km * 15 km in hours and minutes gives 1 hour 30 min

A pace converts to another distance or to a speed with in, and a speed converts back to a time per distance:

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5:00/km in min/mi gives 08:03/mi

5:00/km in km/h gives 12 km/h

10 km/h in min/km gives 6 min/km

The distance in duration form only produces a pace when the first quantity is a distance and the second a duration. Between other quantities, in followed by a number counts how many of the second fit into the first, as a plain number: 1 hour in 3 seconds gives 1,200 and 2 meters in 3 feet gives 2.1872265967. For an ordinary conversion, leave the number off the target unit.

Fuel economy

Varlig understands the three common ways to measure fuel economy: kilometres per litre (km/L), litres per 100 kilometres (L/100km, or l/100km) and miles per gallon (MPG, or mpg). Divide a distance by the fuel used to get km/L, and convert between the three with in:

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640 km / 40 L gives 16 km/L

640 km / 40 L in L/100km gives 6.25 L/100km

12.5 km/L in L/100km gives 8 L/100km

6 L/100km in MPG to 1 dp gives 39.2 MPG

45 MPG in L/100km to 1 dp gives 5.2 L/100km

MPG uses US gallons. For the figure a UK car brochure quotes, write UK mpg, imperial mpg or mpg (UK), and convert in either direction:

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30 UK mpg in L/100km gives 9.4160312111 L/100km

6 L/100km in UK mpg to 1 dp gives 47.1 UK MPG

39.2 MPG in UK mpg to 0 dp gives 47 UK MPG

A plain mpg stays US, and mi/UK gal means the same as UK mpg.

Fuel consumption times a distance is the fuel you’ll use, economy times a volume is the distance you can travel, and a distance divided by the economy is the fuel again. The order of the two doesn’t matter, and you can carry on to a cost:

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6 L/100km * 350 km gives 21 L

350 km * 6 L/100km gives 21 L

16 km/L * 45 L gives 720 km

405 miles / 45 MPG gives 9 gal

6 L/100km * 350 km * £1.50/L gives £31.50

Transfer time

Download and upload times use the phrase time to download SIZE at SPEED (or time to upload), which answers in hours, minutes and seconds. You can also divide the size by the speed. To choose the unit yourself, convert with in, putting the phrase in brackets first:

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time to download 60 GB at 400 Mbps gives 20 min

time to upload 2 GB at 20 Mbps gives 13 min 20 s

(time to download 60 GB at 400 Mbps) in minutes gives 20 min

1 GB / (50 MB/s) gives 20 s

Mind the difference between bits and bytes. Broadband speeds are usually quoted in megabits per second (Mbps), while file sizes and download windows use megabytes (MB, MB/s). There are 8 bits in a byte, and Varlig converts between them:

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100 Mbps in MB/s gives 12.5 MB/s

100 Mbps * 10 min in GB gives 7.5 GB

If you check several files against the same connection, give the speed a name:

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broadband = 80 Mbps gives 80 Mbps

4 GB / broadband gives 6.6666666667 min

4 GB / broadband in seconds gives 400 s

The at and @ operator

X at Y, or X @ Y, means different things depending on what’s on each side:

A pace can be written either way, so 10 km at 5:00/km and 10 km at 5 min/km both come to 50 min, and 1 GB at 50 MB/s is the 20 seconds it takes. A conversion after the phrase converts what came out of it, as in 2 hours at 65 mph in km. Money at money of the same currency says nothing on its own, so £500 at £20 asks you for a price, a rate or a percentage instead.

Speed factors, torque and screen resolution are covered in Cooking, sound, screens and mechanics, frame rates in Video timecodes and frames, and exchange rates in Money and currencies.

Putting it together

Here’s a note for a drive from London to Edinburgh, shared between two people. It works out the time on the road with two breaks, the fuel used and each person’s share of the cost:

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# Drive from London to Edinburgh, sharing costs

distance = 640 km

average speed = 80 km/h

driving = distance / average speed gives 8 hours

driving + 2 * 45 min gives 9 hours 30 min

fuel = 6.5 L/100km * distance gives 41.6 L

petrol price = £1.459/L gives £1.459/L

cost = fuel * petrol price gives £60.69

cost / 2 gives £30.35

Each rate cancels the unit next to it: kilometres divided by km/h leaves hours, L/100km times kilometres leaves litres, and £/L times litres leaves pounds. The pump price keeps all three decimal places, so the cost matches your receipt. If the route changes, edit distance and the time, fuel and cost all follow.