Photos, files and everyday tech

Will the holiday photos fit on the drive, how long is that upload going to take, how much video does a 128 GB card hold, and is the bigger screen actually sharper? Bytes, bits, watt-hours and pixels all behave like any other unit here, so these questions come out as ordinary one-line sums.

Will it fit?

A file size times a count is a total, and a capacity divided by a file size is how many go in.

calcCopy

# A year of photos

photo = 4.2 MB gives 4.2 MB

2,400 * photo in GB gives 10.08 GB

# The phone says 128 GB, minus the system

free = 128 GB - 14 GB gives 114 GB

free / photo gives 27,142.8571428571

# Raw files from the weekend

raw = 32 MB gives 32 MB

640 * raw in GB gives 20.48 GB

# Sizing a backup drive with room to grow

library = 480 GB gives 480 GB

library * 2.5 in TB gives 1.2 TB

1 TB in GB gives 1,000 GB

Kilo, mega, giga and tera all step by a thousand, the way drive makers count them, so 1 TB is 1,000 GB rather than 1,024. Doubling your library and adding a bit is the usual rule for a backup drive, and it says a 2 TB drive will do. See Units and conversions.

How long will it take?

Storage is in bytes and connections are in bits. Dividing one by the other sorts out the factor of eight for you.

calcCopy

# Sending the wedding video

upload = 25 GB gives 25 GB

line = 20 Mbps gives 20 Mbps

upload / line in hours gives 2.7777777778 hours

upload / line in hours and minutes gives 2 hours 47 min

# On a faster connection

upload / 100 Mbps in minutes gives 33.3333333333 min

# The film you want to watch tonight

6 GB / 60 Mbps in minutes gives 13.3333333333 min

# Off an SD card at 90 MB/s

64 GB / 90 MB/s in minutes gives 11.8518518519 min

Mbps is megabits a second and MB/s is megabytes a second, which is the difference that makes downloads feel slower than the number on the box. Adding in hours and minutes gives an answer you can plan an evening around. See Arithmetic with units.

Photos and video by the minute

Video eats space at a steady rate, so one figure tells you everything about the card in your bag.

calcCopy

# 4K at about 350 MB a minute

rate = 350 MB/min gives 350 MB/min

rate * 45 min in GB gives 15.75 GB

# What a 128 GB card holds

128 GB / rate in hours gives 6.0952380952 hours

128 GB / rate in hours and minutes gives 6 hours 6 min

# A two-camera day, plus stills

2 * 3 hours * rate in GB gives 126 GB

900 * 28 MB in GB gives 25.2 GB

# Cards to take

ceil((126 GB + 25.2 GB) / 128 GB) gives 2

A rate times a time is a total and a total over a rate is a time, which covers every question a card can raise. Change rate to 90 MB/min for 1080p and the whole block re-answers itself. See Rates with per and /.

Batteries

A capacity divided by what the thing draws gives how long it lasts.

calcCopy

# Laptop, 72.4 Wh

laptop = 72.4 Wh gives 72.4 Wh

laptop / 8.5 W gives 8.5176470588 hours

laptop / 8.5 W in hours and minutes gives 8 hours 31 min

# Phone, in the units the spec sheet uses

phone = 4,352 mAh gives 4,352 mAh

phone / 380 mA in hours and minutes gives 11 hours 27 min

# A 20,000 mAh power bank

20,000 mAh / phone gives 4.5955882353

# Charging at 30 W

laptop / 30 W in minutes gives 144.8 min

Watt-hours over watts and milliamp-hours over milliamps both leave a time, so whichever way the spec sheet quotes it, the sum is the same shape. The power bank line is the honest answer to “how many charges is that?”, before you take losses off. See Units from a textbook or datasheet.

Screens

Pixels across and down give the megapixels; with the diagonal, they give the sharpness.

calcCopy

2560 x 1440 gives 3.6864M

3840 x 2160 gives 8.2944M

# Pixels per inch on a 27-inch screen

sqrt(2560^2 + 1440^2) / 27 to 0 dp gives 109

sqrt(3840^2 + 2160^2) / 27 to 0 dp gives 163

# A 14-inch laptop at 3024 x 1964

sqrt(3024^2 + 1964^2) / 14.2 to 0 dp gives 254

# Aspect ratios

2560 / 1440 gives 1.7777777778

3440 / 1440 gives 2.3888888889

# How much wider an ultrawide desk needs to be

34 in in cm gives 86.36 cm

The diagonal in pixels comes from Pythagoras, and dividing it by the diagonal in inches gives pixels per inch: 109 for a normal 27-inch screen, 163 for the 4K one, and 254 on a modern laptop. 1.778 is 16:9 and 2.389 is 21:9. See Powers and roots.

The data plan

An allowance is a rate, so it converts into a daily budget like any other.

calcCopy

plan = 15 GB/month gives 15 GB/month

plan in MB/day gives 492.8232612579 MB/day

# Streaming music on the commute

90 min * 2.4 MB/min in GB gives 0.216 GB

# Video calls at about 1.2 GB an hour

5 hours * 1.2 GB/hour gives 6 GB

6 GB is what % of 15 GB gives 40%

# Tethering the laptop for a day

8 hours * 350 MB/hour in GB gives 2.8 GB

is what % of is the line that tells you whether a habit fits in the plan. See What percentage is it?

Make it your own

• Price cloud storage against a drive: £8.99 a month in £/year gives £107.88/year, next to a one-off £120 for 4 TB.
• Check a photo before you print it: 4032 / 300 gives 13.44, so that photo prints 13 inches wide at 300 dpi.
• Size a scan before you start: 8.27 * 600 gives 4,962 pixels across an A4 page at 600 dpi, and 2.5 MB * 40 in MB gives the 100 MB the finished PDF will weigh.
• Work out a subscription stack: total your #subscriptions tagged lines and convert with in £/year. See Tags.
• Convert a bitrate the way an export dialog writes it: 8 Mbps * 12 min in MB gives 720 MB.
• See what a device costs to run: 5 W * 24 hours * 365 * 24.5p/kWh gives the year on a always-on gadget.
• Check a refresh rate against a frame time: 1 / 120 Hz in ms gives 8.33 ms.
• Compare RAM and storage honestly: 16 GiB in GB gives 17.179869184 GB, which is why the two numbers never quite match.
• Plan a phone upgrade: £999 in 24 instalments gives £41.63 a month to compare against a contract.
• Work out a print size in centimetres: 6 x 4 in in cm converts each side, 15.24 × 10.16 cm.
• See how long a podcast backlog really is: sum([42 min, 55 min, 1 hour 12 min]) gives 2 hours 49 min. See Lists with units.