Loki for the Web

Entry Unit no unit Distance Angstrom unit micron mil caliber point, printers pica, printers inch hand link, surveyor feet ' " (feet and inches) link, engineer cubit stud yard megalithic yard meter ell Smoot fathom rod chain, surveyor chain, engineer furlong cable km mile nautical miles league astronomical unit light-year parsec Area barn circular mil in^2 tile, 1x1 tile, 2x2 tile, 4x4 face brick paver brick tile, 6x6 tile, 8x8 block ft^2 tile, 12x12 tile, 18x18 yd^2 m^2 sheet, 4x8 roof bundle wallpaper roll paint gal are acre hectare km^2 mi^2 section township Volume micron^3 ml (milliliter) dram tsp (teaspoon) tbsp (tablespoon) in^3 floz (fluid ounce) gill, US gill, UK cup pint, US liquid pint, US dry quart, US liquid l (litre) quart, US dry board-ft gal, US liquid gal, US dry gal, UK liquid peck ft^3 bushel barrel, US dry barrel, US liquid barrel, oil hogshead gravel ton cord-ft yd^3 m^3 stere cord acre-ft km^3 mi^3 Mass carat gram scruple gram, av dram gram, troy grain oz, av oz, troy lb, troy lb, av kg (kilogram) stone slug hweight, 100 hweight, 112 ton mton (metric ton) Angle grad deg (degrees of arc) deg:min:sec ra (Right Ascention) rad (radians) Time sec (seconds) : : (HH:MM:SS) min hr day week fortnight lunation yr century Date y (date) Temperature oC (deg Celsius) oF (deg Farenheight) K (Kelvins) oR (deg Rankin) Speed kph (km per hour) fps (feet per second) mph (miles per hour) knots mps (meters per sec) fpf (furlongs/fortnight) Data GBy (GigaBytes) MBy (MegaBytes) KBy (kiloBytes) By (bytes) ny (nybbles) bit (bits) Data Rate Byps (Bytes/second) bps (bits/second)

Loki L   T Z Y X   Entry Fractions Mode off fixed denom.. factors of denom. most precise denominator radix . radix ,

Show no unit Distance Angstrom unit, 1e-10m micron, 1e-6m mil, 1/1000 in caliber, 1/100 in point, printers pica, printers inch hand, 4in link, surveyor, 7.92in ft (feet) ' " (feet and inches) link, engineer, 12in cubit stud, 16in megalithic yard yard m (meters) ell Smoot fathom, 6ft rod chain, surveyor chain, engineer furlong cable km mi (miles) nmi (nautical miles) league (int'l nautical, 3nmi) astronomical unit, IAU light-year parsec, IAU Area barn, 1e-28m^2 circular mil in^2 tile, 1x1 tile, 2x2 tile, 4x4 face brick, 21in^2 paver brick, 32in^2 tile, 6x6 tile, 8x8 block, 128in^2 ft^2 tile, 12x12 tile, 18x18 yd^2 m^2 sheet, 4x8 roof bundle, 33.33ft^2 wallpaper roll, 56ft^2 paint gal, 350ft^2 are acre hectare, 1e4m^2 km^2 mi^2 section townshp Volume micron^3 ml (milliliter) dram, fluid US tsp (teaspoon) tbsp (tablespoon) in^3 floz (fluid ounce) gill, US gill, UK cup pint, US liquid pint, US dry quart, US liquid l (litre) quart, US dry board-ft, 144 in^3 gallon, US liquid gallon, US dry gallon, Uk liquid peck ft^3 bushel barrel, US dry, 105dry qt barrel, US liquid, 31.5gal barrel, oil, 42gal hogshead gravel ton, .77yd^3 cord-ft, 16ft^3 yd^3 m^3 stere cord acre-ft km^3 mi^3 Mass carat gram scruple gram, avoirdupois dram gram, troy grain ounce mass avoirdupois ounce mass troy lb (pound mass troy) lb (pound mass avoirdupois) kg (kilogram) stone slug hundredweight, 100lbs hundredweight, 112lbs ton mton (metric tons) Angle grad deg (degrees of arc) deg:min:sec ra (Right Ascention) rad (radians) Time sec (seconds) : : (HH:MM:SS) minute hour day week fortnight lunation, 42,532min year century Date y (date) Temperature oC (deg Celsius) oF (deg Farenheight) K (Kelvin) oR (deg Rankin) Speed kph (km per hour) fps (feet per second) mph (miles per hour) knots mps (meters per sec) fpf (furlongs/fortnight) Data GBy (GigaBytes) MBy (MegaBytes) KBy (kiloBytes) By (bytes) ny (nybbles) bit (bits) Data Rate Byps (Bytes/second) bps (bits/second)

Notes

Loki operates as a standard RPN calculator. However, it's extended capabilities take a little explaining. These capabilities fall into the areas of input, operators, and display.

Loki's unit operations are designed to make life easy in situations which you come across in the real world. For example, you can square a distance unit to get an area. However, if you enter nonsense, you'll get nonsense back: adding a mass to an angle gives a result, but probably not a useful one.

Input

Numbers With Units

Essentially, you enter numbers as you would expect to. For example, if the input units were deg:min:sec, you could enter the value 45 degress 30 minutes 14 seconds a value as:

4 5 u 3 0 u 1 4

Note that the u key represents any units separator. If a value has only one separator (e.g., feet and inches), you use u once. If a value has two separators (e.g., h:m:s), you use u twice. If the unit has no separators (e.g., inches), you don't use the u key.

Each of the numbers (45, 30, and 14) is itself entered as an arbitrary fraction. The three values are scaled internally before being converted to standard form. In this example, the program does:

45 + 30/60 + 14/3600

...and the whole value converted to radians (the standard angle form).

Fractions

Any value can be entered as a fraction. Fractional values are entered as:

integer a^b/c numerator a^b/c denominator

Again, each of the integer, numerator, and denominator values can be an arbitrary number. The program performs the obvious calculation (integer + numerator/denominator) to determine the value.

If any of the components are missing, the program supplies defaults according to the following table.

Arbitrary Numbers

Numbers are what you would expect:

• an optional +/-,
• zero or more digits,
• an optional radix mark,
• zero or more digits,
• an optional EEX,
• if the EEX is present, an optional +/-, and
• zero or more digits.

These combinations permit some weird results: you can have up to three of each form of fraction mark in a number, and up to 9 radix and/or EEX marks!

Operators

All of the operators work in the obvious manner: + performs * addition, performs multiplication, etc. However, some have special properties when used with certain unit groups. These special combinations are listed in the following table.

The diagonal operator (the triangle with the black hypotenuse) computes the length of the diagonal, given the two sides in X and Y.

Display

Values are stored internally in a standard form along with their type group information. For example, all distance values are stored in meters and all mass values are stored in kg. (Well, except for temperatures, which are special-cased: see the preceeding section.)

When a value is displayed, the program iterates over all units in that group. It converts to and displays each checked unit. If no units are checked, it is displayed without a unit. Careful observation will show that the display unit(s) are completely separate from the input unit.

When a value is displayed, it can be displayed in one of four ways. For these examples, a value of 1.76 and a denominator of 8 will be used.

• As a decimal value: you see 1.76.
• As a fraction in fixed denominator mode. The specified denominator will be used. You will see 1 6/8^. The "^" character means that the true value is higher than shown. (A "v" character is sued when the true value is lower.)
• As a fraction in factors of denominator mode. The specified denominator will be used, but the fraction will be reduced to its simplest form. You will see 1 3/4^.
• As a fraction in most precise mode. The most precise mode tries all denominators to find the closest match. In this example, the value 1 3/4^ would be seen. If the denominator was 100, the value 1 38/50 would be seen.

Notes

The megalithic yard (0.83m) was devised by Alexander Thom (1894-1985). More information can be found at http://www.britannia.com/wonder/thom.html.