Measurement {measurement} requires starting point or baseline value and ending point. Measurements use unit measures. Measurement counts number of units between starting and ending points. Measurement requires measurement units. Measurements use length, mass, and time units {fundamental units}.
Measurement depends on standard values {measurement unit} {unit of measurement}.
All other units combine length, time, and mass units {fundamental unit}| {absolute unit}. The seven fundamental SI units are length {meter, length unit}, time {second, time unit}, mass {kilogram, mass}, electric current {ampere}, thermodynamic temperature {Kelvin, thermodynamic temperature}, substance amount {mole, particle number}, and light intensity {candela, light intensity}.
derived units
The 22 derived SI units are plane angle {radian, plane angle}, solid angle {steradian, angle}, force {newton}, pressure {pascal}, energy {joule}, power {watt}, temperature {Celsius, temperature}, electric charge {coulomb, electric charge}, electric potential {volt}, electric capacitance {farad}, electric resistance {ohm}, electric conductance {siemens}, magnetic flux {weber}, magnetic flux density {tesla}, magnetic inductance {henry}, light flux {lumen, light flux}, illuminance {lux}, frequency {hertz}, rates and radioactivity {becquerel, radioactivity rate}, radiation dose {gray} {sievert}, and catalytic activity {katal}.
If constants c, G, k are set equal to 1, so c = G = k = 1, all measurements are in centimeters or inverse centimeters {geometrized unit}|. Length uses cm, time uses cm^-1, and mass uses cm^5. The basis for geometrized units is that time and distance relate by constant light speed. Mass, time, and length relate, because photons have different energies at different frequencies, and time relates to frequency. Fundamental units can be velocity, expressed as centimeters per second, or time, expressed as seconds.
To convert unit to another unit {conversion of units} {unit conversion}, multiply original measurement by new-unit to original-unit ratio, obtained from reference books, to cancel original unit and leave new unit. For example, to convert meters to centimeters, (15 meters) * (100 centimeters/meters) = 1500 centimeters.
Unit systems {metric system}| can use meter for length, kilogram for mass, and second for time {meter-kilogram-second system} (MKS), or centimeter for length, gram for mass, and second for time {centimeter-gram-second system} (CGS).
World standard measurement system {Systeme Internationale} (SI) is metric system.
English measurement system {Imperial measure} is in USA.
Prefixes {prefix, measurement} represent powers. 10^24 {yotta} (Y). 10^21 {zetta} (Z). 10^18 {exa} (E). 10^15 {peta} (P). 10^12 {tera} (T). 10^9 {giga} (G). 10^6 {mega} (M). 10^3 {kilo} (kg). 10^2 {hecto} (h). 10^1 {deca} (da). 10^-1 {deci} (d). 10^-2 {centi} (c). 10^-3 {milli} (m). 10^-6 {micro} (µ). 10^-9 {nano} (n). 10^-12 {pico, measurement} (p). 10^-15 {femto} (f). 10^-18 {atto} (a). 10^-21 {zepto} (z). 10^-24 {yocto} (y).
The iso- prefix {iso-, measurement} means the same at different locations. Isobar is for pressure. Isobath is for depth. Isocline is for magnetic dip. Isogon is for magnetic declination. Isohaline is for ocean-surface salinity. Isohel is for hours of sunshine. Isohyct is for rainfall. Isoseismal is for earthquake shock. Isotherm is for temperature. Isochronous is for time.
Measurement digits have different importance {significant figure}| {significant digit}. Zeroes to left of left-most non-zero digit are not meaningful. If number has no decimal point, zeroes to right of right-most non-zero digit are not meaningful. If number has decimal point, zeroes to right of right-most non-zero digit are meaningful. Zeroes between non-zero digits are meaningful.
instruments
Number of significant digits is number of measured digits, including estimated digit.
products
For calculation results, number of significant digits is smallest measured number of significant digits. Multiplying or dividing measurements must maintain number of meaningful digits.
Analyses have number of significant figures {accuracy}|.
Analog-instrument sensitivity {precision}| is tenth of distance between marks. For example, ruler with millimeter markings has precision tenth of millimeter. Digital-instrument precision is displayed numbers.
Quantitative analyses have variability range. Repeated measurements must have similar results {reproducibility}|. If repeated measurement results in significantly different values, results are not reproducible.
Quantitative analyses can detect substance from among other materials {selectivity, measurement}|. For example, instruments detect one frequency or smaller or larger frequency range.
Quantitative analyses have minimum detectable amount {sensitivity, measurement}|. For example, instruments detect intensity threshold.
Precise-measurement technique {nulling}| cancels unknown values using known standard or sensed values using expected values. Nulling methods do not require apparatus to be linear.
Quantities {extensive quantity}| can be sums or differences over time or space ranges. They are total amounts: distance, area, volume, time interval, moles, energy, heat, entropy, charge, and mass. They have magnitude but no direction. Measuring extensive quantities requires accumulation. Extensive quantities are intensive-quantity integrals.
Quantities {intensive quantity}| can be values at times and places. They are instantaneous or local amounts, amount changes, or measurement ratios. Temperature, time, rate, concentration, and chemical potential are scalar magnitudes, with no direction. Distance, direction, velocity, acceleration, force, pressure, momentum, and intensity are vector quantities, with magnitude and direction. Intensive quantities can be matrices. Measuring intensive quantities requires comparing two points over time or distance, to make an extensive quantity. Intensive quantities are extensive-quantity differentials. For example, thermometers measure temperature by linearly expanding mass.
People {people measurements} are 1 meter tall, weigh 10^5 grams, and live 10^10 seconds. Head volume is 1 liter. Heartbeat force is 1 newton. Heartbeat work is 1 joule. Heartbeat power is 1 watt. Walking speed is 2 meters per second. Every day, people make 8000 J or 2000 Calories. Human internal temperature is 37 C. Room temperature or human surface temperature is 21 C. After walking across wool rug, charge on finger is 1 Coulomb.
Number measures {number measurement} include 12 {dozen}, 144 {gross}, and Avogadro's number 6.02 x 10^23 {mole, number} (mol).
Cloth threads {cloth measurement} have units {denier}. Denier range is 100 to 350.
Cycles divided by time in seconds {cycles per second} (Hertz) (Hz) is frequency {frequency measurement}. Frequency is always a positive number. Alternating current is 50 Hz or 60 Hz.
Mechanical-object frequencies measure revolutions per minute (rpm). Car internal-combustion engines operate at 700 rpm to 6500 rpm.
Lowest frequency is one cycle during age of universe, 1/(10^21 s) = 10^-21 Hz. Lowest practical electromagnetic-wave frequency is 1 Hz (with wavelength 10^8 meters, one light-year).
By quantum mechanics, highest frequency {Planck frequency} is inverse Planck time 1/(10^-43 s) = 10^43 Hz. Highest practical electromagnetic-wave frequency is 10^23 Hz (with wavelength 10^-15 meters, electron diameter).
500 sheets {ream} is paper-quantity unit {paper measurement}.
Many different units {becquerel, radioactivity} {roentgen} {rad} {dose equivalent} {rem} {curie} measure radioactivity {radioactivity measurement}.
Electric-charge units {charge measurement} are one mole of electrons {faraday} (F) or total charge {coulomb, charge} (C) moved one meter by one newton. 1 F equals 96494 C.
Electric charge, in coulombs, divided by time, in seconds is electric current {electric current measurement} in amperes (A). Currents are typically 0.1 A to 5 A. Radio current is 1 A.
Electric energy, in joules, divided by charge, in coulombs, is electric potential {potential measurement} in volts (V). Small-battery voltage is 1.5 V. Car-battery voltage is 12 V. Magnetic field has unit {gauss}.
Electric potential, in volts, divided by current, in amperes, is electrical resistance {resistance measurement} in ohms, which has upper-case omega symbol.
Electric-potential change divided by current change is electric capacitance {capacitance measurement} in farads (F). Capacitors have farad range from 1 F to 500 F.
Electric-current change divided by electric-potential change is electrical inductance {inductance measurement} in henrys.
In metric system, fundamental mass units {mass measurement} are gram {gram} (g) or kilogram {kilogram, mass unit} (kg). A derived mass measure is 1000 kilograms {tonne}. Atom mass unit is 10^-24 grams {atomic mass unit}, 1/12 of carbon-12 atom mass. Mass unit in English units is slug {slug, mass}.
Mass, in kilograms, times acceleration, in meters per second squared, is force unit {force measurement} in newtons (N), in MKS system. Mass, in grams, times acceleration, in centimeters per second squared, is force unit {dyne} in CGS system.
Mass times gravity acceleration is weight. In English measure, weight measurements use different systems, depending on mass range.
avoirdupois
In avoirdupois units {avoirdupois}, 28.35 grams is 1 ounce {avoirdupois ounce}. Avoirdupois weights include 16 avoirdupois ounces {avoirdupois pound} {pound, weight}, 100 avoirdupois pounds {hundredweight}, 2000 avoirdupois pounds {ton, weight}, 1/16 avoirdupois ounces {dram}, 1/7000 avoirdupois pounds {grain, mass unit}, 100 avoirdupois pounds {cental}, 100 avoirdupois pounds or 112 avoirdupois pounds or 100 kilograms {quintal}, and 2240 avoirdupois pounds {long ton}.
apothecary
Apothecary weights {apothecaries measure} depend on 1 grain {apothecary grain}. Apothecary weights include 20 apothecary grains {apothecary scruple}, 3 apothecary scruples {apothecary dram}, 8 apothecary drams {apothecary ounce}, 12 apothecary ounces {apothecary pound}. Apothecary pound has same weight as troy pound.
troy
Troy weights, based on 1 grain {troy grain}, are for weighing gold, silver, and jewels. Troy weights include 24 troy grains {troy pennyweight}, 20 troy pennyweight {troy ounce}, and 12 troy ounce {troy pound}.
electromagnetism
Electric force is in newtons. Magnetic force has units {unit pole}.
Force, in newtons, times distance, in meters, is work and energy {energy measurement} in joules (J), in MKS system. Force, in dynes, times distance, in centimeters, is energy unit {erg} in CGS system. 10000 erg equals 1 joule.
In English measure, force is weight, in pounds, times distance, in feet {foot-pound}.
electric
Voltage, in volts, times charge, in coulombs, is electric energy in joules. For subatomic particles, electric energy is voltage, in volts, times electron charge {electron-volt} (eV). Electric energy is power, in kilowatts, times time, in hours {kilowatt-hour}. USA houses use hundreds of kilowatts each month.
heat
Heat energy is energy needed to heat one gram of water one degree Celsius {calorie} (cal) or one kilogram of water one degree Celsius {Calorie} (Cal). 1 Cal = 1000 cal. In English measure, heat energy uses larger units {British thermal unit} (BTU).
Temperature units {temperature measurement} relate to water freezing and boiling temperatures. In Kelvin (K), freezing point is 273 degrees and boiling temperature is 373 degrees. In Celsius (C), freezing point is 0 degrees and boiling temperature is 100 degrees. In English measure {Fahrenheit} (F), freezing point is 32 degrees and boiling temperature is 212 degrees. An English temperature measure {Rankine} is Fahrenheit plus 459.69 degrees.
Force, in dynes, times time, in seconds {dyne-second}, is impulse, impact, or action {impulse measurement}.
In SI system, power per area {intensity measurement} can be power per steradian. Informally, intensity is flux per steradian, pressure divided by time, or force per second per unit distance.
Sound intensity uses logarithmic scale {bel}, or its tenths {decibel} (db) (dB), so 10 db equals 1 bel. Whispers are 30 db. Siren loudness is 100 dB. Larger units {neper} are 6.686 db.
Light intensity compares to standard candle {candela, intensity} (cd) {international candle} {candle, light} {lumen, light}. One candela is light intensity 1/683 watts per steradian, at frequency 540 * 10^12 hertz.
Energy, in joules, divided by time, in seconds, is power {power measurement} in watts (W). In refrigeration, 3517 watts are one ton {ton, refrigeration}. In English measure, power compares to standard horse power {horsepower}.
Mixing alkanes and benzenes makes gasoline {gasoline measurement}, which has engine power {octane number}. Octane is 87 for regular gas, 89 for intermediate gas and 91 for premium gas.
Force, in newtons, divided by area, in square meters, is pressure {pressure measurement} in pascals. Atmospheric pressure has pressure units {bar, pressure unit} {atmosphere, pressure unit} (atm). Pressure is how high mercury rises in columns {torr} {mm Hg} {inches Hg}. 1 atm equals 760 mm Hg. Standard temperature and pressure (STP) is 25 C and 1 atm. In English measure, pressure is force, in pounds, divided by area, in square inches {pounds per square inch} (psi).
Mass, in grams, divided by volume, in cubic centimeters, is density {density measurement}: d = g/cm^3. Water density is 1 g/cm^3.
Metals {gold measurement} can have purity {karat} (K). 28 K is pure. 24 K is high purity. 18 K is good purity. 14 K is strong. 10 K is strongest.
Dynamic-viscosity unit {poise, viscosity unit} differs from kinetic-viscosity unit {myriastoke} {viscosity measurement}.
Space measurement {length measurement} {distance measurement} uses distance units. The MKS system has a fundamental length unit {meter, length} (m). Derived length units include 10^-2 meters {centimeter}, 10^-6 meters {micron}, and 10^-10 meters {Angstrom}.
English measure
0.001 inches (mil) measures wire diameter. 2.54 centimeters {inch} (in). 39.37 inch = 1 meter. 0.66 feet {li, length unit}. 3 inches {palm, length}. 4 inches {hand}. 7 to 9 inches {span}. 12 inches {foot, length} (ft). {board foot}. 18 inches to 22 inches {cubit}. 2.5 feet {pace, length}. 3 feet {yard, length} (yd). 6 feet {fathom}. 16.5 feet {rod, measure}. 100 links or 66 feet {chain, length} {Gunter's chain} {surveyor's chain}. 100 feet or 100 links {chain} {engineer's chain}. 625 Greek feet or 0.1196 mile {stade}. 220 yards {furlong}. 5280 ft, 1760 yards, 8 furlongs, or 1.609 kilometers {mile} {statute mile}. 1 arc-minute on great circle of sphere with area equal to Earth area is 6080 feet {nautical mile}. 1 arc-minute at equator is 6087 feet {geographic mile}. 3 miles, or 2.4 to 4.6 miles {league}.
railroad
Railroad track {railroad measurement} has width {standard gauge} {narrow gauge} {HO guage}.
wire gauge
Wires have diameters {wire gauge}, such as American or Brown and Sharpe system.
minimum
By quantum mechanics, minimum length is Planck length, 1.6 * 10^-35 meters, where length becomes quantized.
maximum
Maximum length is circumference of universe, 10^30 meters.
Length, in meters, divided by time, in seconds {meters/second}, is velocity {speed measurement}. In English measure, velocity is miles per hour (mph) or nautical miles per hour {knot, speed}. Velocity divided by time, in seconds {meters/second squared}, is acceleration. Earth-gravity acceleration is 9.8 m/s^2. Car acceleration is 3 m/s^2 or 1/3 gravity.
Surface measurement {area measurement} is length squared or square meters (m^2). Area measure can be 1000 m^2 {hectare}, which is 2.5 acres. In English measure, area can be 10 square chains, 160 square rods, or 0.4047 hectare {acre} or can be 36 square miles {township}. 640 acres equals 1 square mile. For cross-sections {cross-sectional area}, 1 barn is 10^-28 cm^2.
Space measurement {volume measurement} depends on length measurement. Length cubed is in cubic meters. Volume measure is 1000 cm^3 or 0.001 m^3 {liter} (L).
English measure
1/360 fluid ounce {minim}. 1/6 fluid ounce {teaspoon} (tsp). 3 teaspoons {tablespoon} (tbsp). 2 tbsp {fluid ounce} (fl oz). 1 1/2 fl oz {jigger}. 0.25 pint or 4 fluid ounces {gill, volume}. 8 fluid ounces {cup}. 2 cups or 16 fluid ounces {pint}. 1/16 peck {dry pint}. 2 pints or 1.1 liter {quart, volume}. 1/8 peck {dry quart}. 4 quarts {gallon}. gallon slightly larger than regular gallon {Imperial gallon}. {stere}. 0.25 bushel {peck}. 0.3524 hektaliter {bushel}. 1/4 barrel or 9 gallons {firkin}. 31.5 gallon {barrel, volume unit}. {demijohn}. 2 barrels {hogshead}. 3000 ml or four-fifths gallon {double-magnum} {jeroboam}, for wine. two-wine-bottle or 1500 ml {magnum, champagne}. {split}. {trencher}. 128 ft^3 {cord, volume}. hay {bale}.
Two intersecting lines have opening amount {angle measurement} at intersection. If lines are the same, angle between them is 0 degrees, and angle around them is 360 degrees, two times pi radians. If lines are parallel and meet at center, angle between them is 180 degrees, pi radians. If lines are perpendicular, angle between them is 90 degrees, pi/2 radians. Angle measure can use larger unit {rhumb}, which is 11.25 degrees, 1/16 of reverse turn, or one point on mariner's compass.
Metal wires have diameters {gauge, measurement}. Smaller numbers are larger diameters.
Aperture size {opening measurement}, as for camera lens, has units {f number} {f stop}. f stops are numbers 2 for wide open, 2.8, 4, 5.6, 8, 11, 16, 22, and 32 for almost closed.
Earth locations have distances and elevations {surveying measurements}. Measured great-circle arc {level, survey} can be surveying basis.
Finding elevation difference uses instrument {level, instrument} {spirit level}| that measures angles.
High objects have angle {acclivity} to horizontal.
Low objects have angle {declivity} to horizontal.
Surveying instruments {theodolite}| can measure horizontal and vertical angles.
Observers above ground can see Earth surface out to distance {horizon, Earth}. If Earth is spherical, horizon relates to height above ground: r = 1.23 * h^0.5, where r is radius from observation point to horizon, and h is height above ground.
Surveyors place metal plates {benchmark, surveying}| at locations with precise elevation.
Measuring time {time measurement} requires standard vibration or rotation frequency. Fundamental time unit is one second {standard second} {SI second} (s), which is 9,192,631,770 periods of unperturbed microwave transition between two cesium-133 ground-state hyperfine levels, as measured by atomic clocks {Coordinated Universal Time} (UTC).
year
Standard second can depend on Earth motion around Sun. Tropical year 1900 has 31,556,925,974 seconds {ephemeris second} {ephemeris time} {Newtonian time}. Gravity predicts solar-system object positions at distinct times. Ephemeris time uses actual number of days {universal time} (UT0) or universal time corrected for Earth-axis wobble {navigator's time} (UT1) (UT2).
derived units
60 seconds {minute, time} (min). 60 minutes {hour} (hr). 24 hours {day}. 7 days {week}. 14 days and nights {fortnight}. 4 1/3 week or 28 to 31 days {month}. 365 days {year} (yr). 366 days every fourth year {leap year}. 10 years {decade}. 100 years {century, time}. 1000 years {millennium}. 1,000,000 years {eon}.
minimum
By quantum mechanics, minimum time is Planck time, 10^-43 seconds, where time becomes quantized.
maximum
Maximum time is age of universe, 10^21 seconds.
Earth time measurement can compare to Sun {solar time}. Varying orbital speeds and varying seasons cause Sun-referenced Earth-rotation period to average four minutes longer than star-referenced rotation period. Sun-referenced Earth-rotation period can be ahead 16 minutes in early November or behind 14 minutes in early January.
Years {anomalistic year} can be time from Earth perihelion to next perihelion, which is five minutes longer than sidereal years, because major axis of Earth elliptical orbit moves around Sun in same direction as Earth moves.
Years {sidereal year} can be time between same positions with respect to fixed stars. Time {sidereal time} can be relative to fixed stars.
Years {tropical year} can be time from first point of Aries to next first point of Aries, which is 20 minutes shorter than sidereal year, because first point moves around Sun in opposite direction to Earth motion.
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Date Modified: 2022.0225