Units and Canonicalization

SpeedCrunch supports unit-aware arithmetic and conversions. Results are dimensionally consistent and then formatted with readability-oriented canonicalization rules.

Display Policy

The formatter prefers meaningful derived units over full SI base expansion when that improves readability. For example:

• [kg*m*s^(-2)] displays as [N]

• [kg*m^2*s^(-2)] displays as [J]

• [kg*m^(-1)*s^(-2)] displays as [Pa]

When a result is already expressed in a useful derived form, it is preserved:

• 12[J] stays 12[J] (not 12[N⋅m])

• 2[J] + 3[J] displays as 5[J]

• 2[W*h] stays in W⋅h context instead of being expanded unnecessarily

• 1[Btu] stays 1[Btu] instead of being converted to joules

• 1[in] stays 1[in] instead of being converted to metres

SpeedCrunch also avoids forcing a semantic choice when dimensions are equivalent but context differs. A common example is N⋅m: it can represent torque, while J typically represents energy. Without an explicit conversion request, SpeedCrunch preserves authored intent rather than silently replacing one with the other.

When negative exponents appear together with positive ones, SpeedCrunch may render denominator form for readability:

• C⁴⋅m⁴⋅J⁻³ may display as C⁴⋅m⁴ / J³

Unit Notation

In Settings ‣ Results, SpeedCrunch provides a Unit Notation submenu with two display styles:

• Exponential (m·s⁻¹) (default): keeps products with signed exponents, such as kg⋅m²⋅s⁻³.

• Fractional (m/s): moves negative exponents to the denominator when there is at least one positive exponent, such as kg⋅m² / s³.

This is a display preference only; numeric values and dimensions are unchanged.

Authored Units

SpeedCrunch preserves authored units that carry practical or domain meaning. This includes accepted metric units and many non-SI units, such as tonne, hectare, inch, foot, Btu, eV, Eh, bar, atm, psi, Torr, mmHg, hp, kWh, bit, and byte.

For example:

• [tonne] displays as 1 tonne

• [ha] displays as 1 ha

• [Eh] displays as 1 Eh

• [Btu] displays as 1 Btu

This preservation affects display only. Explicit conversion still converts to the requested target:

• [tonne] -> [kg]

• [Btu] -> [J]

• [in] -> [cm]

Time units are handled specially because they also participate in sexagesimal/time display. Use an explicit conversion target when you want a particular time unit display.

When adding or subtracting compatible units, SpeedCrunch may choose a more readable display unit for the result instead of blindly keeping the first operand’s unit. For example, a tiny tonne value added to kilogram and gram values can display in kilograms:

• 0.00000001[t] + 3.2[kg] + 2342.7[g] displays as 5.54271 kilogram

Larger mass results can still remain in tonnes when that is the more readable display. Explicit conversion remains the way to force a target unit.

Time sums use the same readability principle for explicit time units. Results of at least one hour display in hours; results below one hour but at least one minute display in minutes; smaller results display in seconds. Sexagesimal expressions keep their dedicated sexagesimal display behavior.

For units that support SI prefixes, SpeedCrunch also uses a best-fit engineering prefix when the unprefixed unit would make the displayed number unnecessarily large or small. The chosen prefix aims to keep the numeric part in a readable range, typically from 1 up to but not including 1000:

• 1[ps] displays as 1 ps

• 0.0001[s] + 0.89999[ms] + 1[ns] + 1[ps] displays as 999.991001 µs

• 0.0001[s] + 0.899999[ms] + 1[ns] + 1[ps] displays as 1.000000001 ms

• 0.0001[m] + 0.899999[mm] + 1[nm] + 1[pm] displays as 1.000000001 mm

• 0.1[m] displays as 100 mm, not 1 dm

• 0.01[m] displays as 10 mm, not 1 cm

• 0.1[g] displays as 100 mg

• 0.1[L] displays as 100 mL

• 0.1[s] displays as 100 ms

• 0.1[Pa] displays as 100 mPa

This prefix selection is not limited to time units. It applies to supported SI-prefixable units across dimensions, while still respecting special display rules such as hours/minutes/seconds for ordinary time sums and explicit conversion targets requested with -> or in. The small SI prefixes d, c, da and h are accepted for input where supported, but SpeedCrunch does not choose them automatically for result display.

In scientific notation mode, SpeedCrunch keeps the power of ten in the numeric part and displays a single SI-prefixable unit with its unprefixed base symbol:

• 0.0000000001234234235234[m] displays as 1.234234235234 × 10⁻¹⁰ m, not 1.234234235234 × 10² pm

Scientific notation displayed with a multiplication sign and superscript exponent can be reused in unit expressions. For example, 1 × 10⁻¹²[s] is interpreted like 1e-12[s] and displays as 1 ps.

Composed Units

For products and quotients, SpeedCrunch keeps authored composite structure where possible, unless a clear canonical derived target is recognized.

Examples that canonicalize:

• V*A -> W

• F*V -> C

• V*s -> Wb

• T*m^2 -> Wb

• Pa*m^2 -> N

• J/s -> W

Examples that preserve composite intent:

• J*Pa remains a composed derived expression, because there is no single broadly expected named SI derived unit for this product and preserving the authored structure is more readable than base expansion.

• N*W remains a composed derived expression for the same reason: no common canonical named unit is generally expected by users for this product.

• W*h remains in W⋅h form because it is a common domain unit for energy usage; preserving h keeps the practical meaning users typically intend.

• km/h displays as kph and mi/h displays as mph instead of being expanded to m⋅s⁻¹. Speed units are usually chosen for domain readability, so SpeedCrunch preserves common authored speed forms when they match a supported named unit.

• nmi/h displays as knot for the same reason.

Preserved display forms are still normal units. Use explicit conversion when you want another expression:

• [km/h] -> [m/s]

• [mph] -> [km/h]

Conversions

Use explicit conversion to request a specific target unit expression:

• [N*m] -> [J]

• [J/s] -> [W]

• [V] -> [J/C]

• 10[m] in [cm]

• 10[m] -- [cm]

SpeedCrunch supports three equivalent conversion operators: ->, in (keyword alias), and -- (shortcut alias).

If no explicit conversion target is requested, SpeedCrunch applies the canonicalization/display policy above.

Built-in Units Table

Built-in Units by Quantity

Column meanings:

• Canonical name: long built-in unit name.

• Symbol: primary unit symbol.

• Symbol aliases: accepted alternate symbols/aliases.

Absorbed Dose

Canonical name	Symbol	Symbol aliases
gray	Gy	—

Activity Referred To A Radionuclide

Canonical name	Symbol	Symbol aliases
becquerel	Bq	—

Amount Of Heat

Canonical name	Symbol	Symbol aliases
british_thermal_unit	Btu	—
calorie	cal	—
joule	J	—
kilowatt_hour	kWh	—
quad	quad	—

Amount Of Substance

Canonical name	Symbol	Symbol aliases
mole	mol	—

Area

Canonical name	Symbol	Symbol aliases
acre	ac	—
hectare	ha	—
square_foot	ft²	—
square_inch	in²	—
square_kilometre	km²	—
square_metre	m²	—
square_mile	mi²	—
square_millimetre	mm²	—
square_yard	yd²	—

Capacitance

Canonical name	Symbol	Symbol aliases
farad	F	—

Catalytic Activity

Canonical name	Symbol	Symbol aliases
katal	kat	—

Dose Equivalent

Canonical name	Symbol	Symbol aliases
sievert	Sv	—

Electric

Canonical name	Symbol	Symbol aliases
ampere	A	—
coulomb	C	—
ohm	Ω	—
siemens	S	—
volt	V	—

Energy

Canonical name	Symbol	Symbol aliases
electronvolt	eV	—
hartree_energy_unit	Eh	—
joule	J	—
kilowatt_hour	kWh	—

Force

Canonical name	Symbol	Symbol aliases
newton	N	—

Frequency

Canonical name	Symbol	Symbol aliases
hertz	Hz	—
revolution_per_minute	rpm	—

Illuminance

Canonical name	Symbol	Symbol aliases
lux	lx	—

Inductance

Canonical name	Symbol	Symbol aliases
henry	H	—

Information

Canonical name	Symbol	Symbol aliases
bit	b	—
byte	B	—
hartley	Hart	—
nat	nat	—

Kerma

Canonical name	Symbol	Symbol aliases
gray	Gy	—

Length

Canonical name	Symbol	Symbol aliases
angstrom	Å	—
astronomical_unit	au	—
fathom	fathom	—
foot	ft	—
furlong	fur	—
inch	Inch	—
lightminute	lmin	—
lightsecond	ls	—
lightyear	ly	—
metre	m	—
mile	mi	—
nautical_mile	nmi	—
parsec	pc	—
rod	rd	—
yard	yd	—

Luminous Flux

Canonical name	Symbol	Symbol aliases
lumen	lm	—

Luminous Intensity

Canonical name	Symbol	Symbol aliases
candela	cd	—

Magnetic Flux

Canonical name	Symbol	Symbol aliases
weber	Wb	—

Magnetic Flux Density

Canonical name	Symbol	Symbol aliases
tesla	T	—

Mass

Canonical name	Symbol	Symbol aliases
atomic_mass_unit	u	—
carat	ct	—
dalton	Da	—
grain	gr	—
gram	g	—
karat	Kt	—
kilogram	kg	—
long_ton	long_ton	—
ounce	oz	—
pound	lb	—
short_ton	tn	—
stone	st	—
tonne	t	—

Plane Angle

Canonical name	Symbol	Symbol aliases
arcminute	′	arcmin
arcsecond	″	arcsec
degree	°	deg, ˚
gradian	gon	—
microarcsecond	µas	uas
milliarcsecond	mas	—
radian	rad	—
revolution	rev	—
turn	tr	pla

Power

Canonical name	Symbol	Symbol aliases
horsepower	hp	—
watt	W	—

Pressure

Canonical name	Symbol	Symbol aliases
atmosphere	atm	—
bar	bar	—
millimetre_of_mercury	mmHg	—
pascal	Pa	—
pounds_per_sqinch	psi	—
torr	Torr	—

Radiant Flux

Canonical name	Symbol	Symbol aliases
watt	W	—

Solid Angle

Canonical name	Symbol	Symbol aliases
steradian	sr	—

Speed

Canonical name	Symbol	Symbol aliases
kilometre_per_hour	kph	—
knot	kn	—
mile_per_hour	mph	—

Stress

Canonical name	Symbol	Symbol aliases
pascal	Pa	—

Temperature

Canonical name	Symbol	Symbol aliases
degree_celsius	°C	ºC, oC, degC, Cel, ˚C
degree_fahrenheit	°F	ºF, oF, degF, Fah, ˚F
kelvin	K	—

Time

Canonical name	Symbol	Symbol aliases
day	d	—
hour	h	—
minute	min	—
second	s	—
week	wk	—
century_julian	cy_jul	—
year_julian	a_jul	—
year_sidereal	a_sid	—
year_tropical	a_trop	—

Velocity

Canonical name	Symbol	Symbol aliases
kilometre_per_hour	kph	—
knot	kn	—
mile_per_hour	mph	—

Volume

Canonical name	Symbol	Symbol aliases
barrel_beer_us	bbl_beer	—
barrel_oil	bbl_oil	—
cubic_centimetre	cm³	cc
cubic_decimetre	dm³	—
cubic_foot	ft³	—
cubic_inch	in³	—
cubic_kilometre	km³	—
cubic_metre	m³	—
cubic_mile	mi³	—
cubic_millimetre	mm³	—
cubic_yard	yd³	—
cup	cup	—
cup_imp	cup_imp	—
cup_jp	cup_jp	—
cup_us	cup_us	—
dessert_spoon	dsp	—
fluid_dram_imp	fldr_imp	—
fluid_dram_us	fldr_us	—
fluid_ounce_imp	floz_imp	—
fluid_ounce_us	floz_us	—
gallon_imp	gal_imp	—
gallon_us	gal_us	—
gill_imp	gill_imp	—
gill_us	gill_us	—
litre	L	l
pint_imp	pt_imp	—
pint_us	pt_us	—
quart_imp	qt_imp	—
quart_us	qt_us	—
tablespoon	tbsp	—
tablespoon_au	tbsp_au	—
tablespoon_imp	tbsp_imp	—
tablespoon_us	tbsp_us	—
teaspoon	tsp	—
teaspoon_imp	tsp_imp	—
teaspoon_us	tsp_us	—

Work

Canonical name	Symbol	Symbol aliases
joule	J	—
kilowatt_hour	kWh	—