Units and Canonicalization¶

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¶