Everyday

Kitchen, energy, fitness, and notes: units doing the work so you do not have to.

Scale a recipe and mint a unit for the butter

Cooking mixes metric and US units, and every kitchen has a unit of its own. Declaring one takes a line.

## Cake for twelve, from a recipe for eight
scale = 12 / 8
flour = 250 g * scale
sugar = 175 g * scale
milk = 300 ml * scale to cups to 1 dp
unit stick = 113 g, also: sticks
butter = 175 g * scale
butter to sticks to 1 dp
oven = 180 C to F

to cups converts the scaled volume; unit stick = 113 g teaches smoot the American butter stick, and to sticks works from then on.

What an appliance costs to run

A tariff is a price per unit of energy. Power times time is energy, and the energy cancels against the tariff to leave money.

tariff = £0.28 / 1 kWh
kettle = 3 kW * 4 minutes
kettle to kWh
kettle * tariff
shower = 9 kW * 12 minutes * tariff
shower * 365 to 2 dp
standby = 15 W * 1 year to kWh
standby to 0 dp
standby * tariff to 2 dp

Nothing here is converted by hand. 3 kW * 4 minutes is an energy whatever units you write it in, and * tariff turns it into money.

Race pace, and the same pace over other distances

Dividing a time by a distance gives a pace; multiplying the pace by another distance gives a time back.

race = 10 km
finish = 50 minute
pace = finish / race to minute/km
pace * 5 km to minute
pace * 42.195 km to hour, minute to 0 dp
pace to minute/mile to 2 dp

The dimension of pace is Time over Length, so pace * 42.195 km cancels the length and leaves a time. to hour, minute shows it in two units, and the trailing to 0 dp rounds the minutes.

BMI from either side of the Atlantic

A function with dimension hints accepts any units of the right kind. The result displays in whatever units went in, so convert it once.

bmi(weight: Mass, height: Length) = weight / height^2 to kg/m^2 to 1 dp
bmi(72 kg, 1.78 m)
bmi(160 lb, 5 ft 10 inch)
verdict = if bmi(160 lb, 5 ft 10 inch) < 25 kg/m^2 then "in range" else "check"

5 ft 10 inch is one length. The comparison in verdict is dimension-checked too: comparing against a bare 25 would be an error.

Ladder safety

Trigonometry takes real angles. sin(75 deg) is not the same as sin(75), which would be radians.

ladder = 6 m
angle = 75 deg
height reached = ladder * sin(angle) to 2 dp
base distance = ladder * cos(angle) to 2 dp
solve for safe angle: 6 m * cos(safe angle) = 1.2 m
safe angle to deg to 1 dp

The solve goes through cos, whose inverse smoot knows, and hands back an angle you can convert to degrees.

Notes that stay notes

A document can carry as much prose as you like. Plain lines with no known names in them are ignored; lines with a # are always ignored. Use # when a note mentions a unit or a name you have defined.

## Trip budget
Two nights, leaving Friday.
# Hotel is 140 a night, m is for metres so this line needs a hash
hotel = 2 * €140
trains = 2 * €38
food = 2 * €60
hotel + trains + food

The second line is a note because none of its words are defined. The third would fail without the #, because m is a unit.