From BIPM: Add "quantity kind"

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Length, breadth/width, height, depth are separate quantities, but they can be compared and worked together because they are all about "length".

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According to the concept of "quantity kind" described in the VIM3 definition.

A "quantity kind" (or "general quantity") is "property whose instances can be compared by ratio or only by order." The key point is that individual quantities of the same kind are comparable.

This contrasts with the "quantity " definition defined there.

So:

• a quantity in a quantity kind must be workable together
• all quantities in a quantity kind must have the same dimension

Note that the BIPM SI Digital Reference nor QUDT distinguish the "quantity kind", they only provide quantities.

Content below from Claude after feeding multiple prompts.

Difference from Dimensions

A dimension is a mathematical expression of physical quantities in terms of base dimensions (like length, mass, time), while a quantity kind is a conceptual grouping of quantities that can be meaningfully compared. Here are three examples illustrating this distinction:

Example 1: Energy and Torque

• Same Dimension: Both have dimension M·L²/T² (mass × length² ÷ time²)
• Different Quantity Kinds:
  • Energy (joules) measures the capacity to do work
  • Torque (newton-meters) measures rotational force
  • While mathematically equivalent in dimensions, they represent distinct physical concepts
  • Converting 50 joules of energy to 50 newton-meters of torque is not physically meaningful, even though the numerical values with units can be written similarly

Example 2: Area and Permeability

• Same Dimension: Both have dimension L² (length²)
• Different Quantity Kinds:
  • Area measures the extent of a 2D surface (m²)
  • Hydrodynamic permeability measures how easily fluid flows through porous media (also m²)
  • Despite having identical dimensions, comparing a field with area 100 m² to sandstone with permeability 10⁻¹² m² lacks physical meaning
  • They measure fundamentally different properties despite sharing dimensional units

Example 3: Frequency, Activity, and Angular Velocity

• Same Dimension: All have dimension T⁻¹ (reciprocal of time)
• Different Quantity Kinds:
  • Frequency measures cycles per second (Hz)
  • Radioactive activity measures decays per second (Bq)
  • Angular velocity measures rotation rate (rad/s)
  • While all dimensionally equivalent (1/second), they represent different physical phenomena
  • A radioactive sample with activity 1000 Bq cannot be meaningfully compared to a wave with frequency 1000 Hz

These examples demonstrate that dimension is purely mathematical, while quantity kind considers the physical meaning and comparability of quantities. Two quantities may share the same dimension but belong to different quantity kinds if they represent fundamentally different physical concepts.

Quantity Kinds Classification

Based on the principles that (1) quantities in a kind must be workable together and (2) all quantities must have the same dimension, here is a revised classification:

Dimension L (Length)

Length Kind (NISTd1)

• Length, distance, breadth, height, thickness, radius, diameter, displacement, wavelength, path length, cartesian coordinates, position vector, radius of curvature, radial distance (NISTq1-NISTq13)

Dimension M (Mass)

Mass Kind (NISTd2)

• Mass (NISTq14)

Dimension T (Time)

Time Kind (NISTd3)

• Time, duration, period, time constant (NISTq15-NISTq18)

Dimension I (Electric Current)

Electric Current Kind (NISTd4a)

• Electric current, electric current intensity (NISTq19, NISTq20)

Magnetomotive Force Kind (NISTd4b)

• Magnetomotive force (NISTq21)

Dimension Θ (Temperature)

Thermodynamic Temperature Kind (NISTd5a)

• Thermodynamic temperature (NISTq22)

Relative Temperature Kind (NISTd5b)

• Celsius temperature, Fahrenheit temperature (NISTq23, NISTq24)

Technical Temperature Kind (NISTd5c)

• ITS-90 temperature, PLTS-2000 temperature (NISTq25, NISTq26)

Dimension L² (Area)

Area Kind (NISTd8a)

• Area (NISTq29)

Permeability Kind (NISTd8b)

• Hydrodynamic permeability (NISTq30)

Dimension L³ (Volume)

Volume Kind (NISTd10a)

• Volume (NISTq31)

Section Modulus Kind (NISTd10b)

• Section modulus (NISTq32)

Dimension L/T (Velocity)

Linear Velocity Kind (NISTd11a)

• Velocity, speed, phase velocity, group velocity, speed of propagation of waves (NISTq33, NISTq34, NISTq36, NISTq37, NISTq38)

Angular Velocity Kind (NISTd11b)

• Angular velocity (NISTq35)

Dimension M·L/T² (Force)

Force Kind (NISTd12)

• Force, weight (NISTq39, NISTq40)

Dimension M/(L·T²) (Pressure)

Pressure Kind (NISTd14a)

• Pressure (NISTq41)

Stress Kind (NISTd14b)

• Stress, normal stress, shear stress (NISTq42, NISTq43, NISTq44)

Energy Density Kind (NISTd14c)

• Energy density (NISTq45)

Elastic Modulus Kind (NISTd14d)

• Modulus of elasticity, modulus of rigidity, modulus of compression (NISTq46, NISTq47, NISTq48)

Dimension M·L²/T² (Energy)

Energy Kind (NISTd15a)

• Energy, work, heat, potential energy, kinetic energy, mechanical energy (NISTq49, NISTq50, NISTq51, NISTq52, NISTq53, NISTq54)

Torque Kind (NISTd15b)

• Moment of force, torque, bending moment of force (NISTq55, NISTq56, NISTq57)

Mechanical Function Kind (NISTd15c)

• Lagrange function, Hamilton function (NISTq58, NISTq59)

Dimension M·L²/T³ (Power)

Power Kind (NISTd16a)

• Power (NISTq60)

Radiant Flux Kind (NISTd16b)

• Radiant flux, radiant intensity (NISTq61, NISTq62)

Electrical Power Kind (NISTd16c)

• Apparent power (NISTq63)

Dimension I·T (Electric Charge)

Electric Charge Kind (NISTd17)

• Electric charge, amount of electricity (NISTq64, NISTq65)

Dimension M·L²/(T³·I) (Electric Potential)

Electric Potential Kind (NISTd18)

• Electric potential, electric potential difference, potential difference, electromotive force (NISTq66, NISTq67, NISTq68, NISTq69)

Dimension T⁻¹ (Frequency)

Frequency Kind (NISTd24a)

• Frequency, rotational frequency, angular frequency (NISTq70, NISTq71, NISTq72)

Activity Kind (NISTd24b)

• Activity referred to a radionuclide (NISTq73)

Rate Kind (NISTd24c)

• Damping coefficient, emission rate (NISTq74, NISTq75)

Dimension L²/T² (Specific Energy)

Absorbed Dose Kind (NISTd25a)

• Absorbed dose, specific energy, specific energy imparted (NISTq76, NISTq77, NISTq78)

Dose Equivalent Kind (NISTd25b)

• Various dose equivalents (ambient, directional, personal, organ) (NISTq79, NISTq80, NISTq81, NISTq82)

Kerma Kind (NISTd25c)

• Kerma (NISTq83)

Dimension M/L³ (Density)

Mass Density Kind (NISTd30a)

• Density, mass density (NISTq84, NISTq85)

Mass Concentration Kind (NISTd30b)

• Mass concentration (NISTq86)

Dimension M·L²/(T²·Θ) (Heat Capacity)

Heat Capacity Kind (NISTd39a)

• Heat capacity (NISTq87)

Entropy Kind (NISTd39b)

• Entropy (NISTq88)

Dimension L²/(T²·Θ) (Specific Heat Capacity)

Specific Heat Capacity Kind (NISTd40a)

• Specific heat capacity (NISTq89)

Specific Entropy Kind (NISTd40b)

• Specific entropy (NISTq90)

Dimension M·L²/T (Angular Momentum)

Angular Momentum Kind (NISTd60a)

• Angular momentum, moment of momentum (NISTq91, NISTq92)

Action Kind (NISTd60b)

• Angular impulse, action (NISTq93, NISTq94)

Dimension 1 (Dimensionless)

Refractive Index Kind (NISTd80a)

• Refractive index (NISTq95)

Relative Permeability Kind (NISTd80b)

• Relative permeability (NISTq96)

Strain Kind (NISTd80c)

• Linear strain, shear strain, volume strain (NISTq97, NISTq98, NISTq99)

Poisson Ratio Kind (NISTd80d)

• Poisson number (NISTq100)

Friction Kind (NISTd80e)

• Dynamic friction factor (NISTq101)

Relative Humidity Kind (NISTd80f)

• Relative humidity (NISTq102)

Relative Density Kind (NISTd80g)

• Relative mass density (NISTq103)

Orientation Kind (NISTd80h)

• Rotation, angle (NISTq104, NISTq105)

Count Kind (NISTd80i)

• Number of entities, number of states (NISTq106, NISTq107)

Probability Kind (NISTd80j)

• Probability, statistical weight (NISTq108, NISTq109)

This classification ensures that quantities within each kind both share the same dimension and can meaningfully work together in calculations.

Examples of Quantities Working Together Within Each Kind

These are examples for quantity kinds that have more than one quantities that belong to them, and the examples are meant to showcase how different quantities in the same quantity kind can work together.

1. Length Kind (NISTd1)

Example: Volume of a rectangular box

length (l) = 5 meters
width (w) = 3 meters
height (h) = 2 meters
volume = l × w × h = 5 × 3 × 2 = 30 cubic meters

This shows how different length quantities (length, width, height) work together.

2. Time Kind (NISTd3)

Example: Number of cycles in a process

duration (t) = 60 seconds
period (T) = 0.5 seconds
number of cycles = t/T = 60/0.5 = 120 cycles

This shows duration and period working together.

3. Electric Current Kind (NISTd4a)

Example: Current relationship in a wire

electric current (I) = 5 amperes
current intensity (J) = I/A = 5 A/0.0002 m² = 25,000 A/m²

Where A is cross-sectional area. This shows current and current intensity working together.

4. Relative Temperature Kind (NISTd5b)

Example: Temperature conversion

Celsius temperature (t_C) = 20 °C
Fahrenheit temperature (t_F) = (9/5 × t_C) + 32 = (9/5 × 20) + 32 = 68 °F

This shows how Celsius and Fahrenheit temperatures are mathematically related.

5. Linear Velocity Kind (NISTd11a)

Example: Wave propagation

phase velocity (v_p) = 150 m/s
group velocity (v_g) = v_p - λ(dv_p/dλ) = 140 m/s

Where λ is wavelength. This shows phase and group velocity working together.

6. Force Kind (NISTd12)

Example: Net force on an object

applied force (F) = 100 N (upward)
weight (W) = 80 N (downward)
net force = F - W = 100 - 80 = 20 N (upward)

This shows force and weight working together.

7. Stress Kind (NISTd14b)

Example: Von Mises stress calculation

normal stress (σ) = 150 MPa
shear stress (τ) = 75 MPa
von Mises stress = √(σ² + 3τ²) = √(150² + 3×75²) = 206.2 MPa

This shows normal and shear stress working together.

8. Elastic Modulus Kind (NISTd14d)

Example: Relationship between elastic moduli

modulus of elasticity (E) = 200 GPa
modulus of rigidity (G) = 80 GPa
Poisson's ratio (ν) = (E/2G) - 1 = (200/160) - 1 = 0.25

This shows how different elastic moduli relate.

9. Energy Kind (NISTd15a)

Example: Energy conservation

kinetic energy (KE) = 100 J
potential energy (PE) = 50 J
heat (Q) = 25 J
total energy = KE + PE + Q = 100 + 50 + 25 = 175 J

This shows different energy forms adding together.

10. Torque Kind (NISTd15b)

Example: Resultant torque

moment of force (M₁) = 30 N·m
bending moment (M₂) = 20 N·m
resultant torque (τ) = M₁ + M₂ = 30 + 20 = 50 N·m

This shows moment of force and bending moment working together.

11. Radiant Flux Kind (NISTd16b)

Example: Radiometric relationship

radiant flux (Φ) = 1000 W
solid angle (ω) = 0.1 sr
radiant intensity (I) = Φ/ω = 1000/0.1 = 10,000 W/sr

This shows how radiant flux and intensity relate.

12. Electric Charge Kind (NISTd17)

Example: Charge conservation

initial electric charge (Q₁) = 5 C
amount of electricity transferred (ΔQ) = 2 C
final charge (Q₂) = Q₁ + ΔQ = 5 + 2 = 7 C

This shows electric charge and amount of electricity working together.

13. Electric Potential Kind (NISTd18)

Example: Voltage in a circuit

electromotive force (EMF) = 12 V
potential difference across component (Vₚₐ) = 4 V
remaining potential difference (Vᵣₑₘ) = EMF - Vₚₐ = 12 - 4 = 8 V

This shows EMF and potential difference working together.

14. Frequency Kind (NISTd24a)

Example: Angular frequency calculation

frequency (f) = 60 Hz
angular frequency (ω) = 2π × f = 2π × 60 = 377 rad/s
rotational frequency (n) = f = 60 rotations per second

This shows frequency, angular frequency, and rotational frequency working together.

15. Absorbed Dose Kind (NISTd25a)

Example: Radiation dose calculation

specific energy (z) = 0.01 J/kg
absorbed dose (D) = z = 0.01 Gy

This shows specific energy and absorbed dose are equivalent.

16. Dose Equivalent Kind (NISTd25b)

Example: Radiation protection

personal dose equivalent (Hp) = 5 mSv
ambient dose equivalent (H*) = 5.5 mSv
effective dose (E) = (Hp + H*)/2 = (5 + 5.5)/2 = 5.25 mSv

This shows different dose equivalents working together.

17. Mass Density Kind (NISTd30a)

Example: Average density calculation

density of material 1 (ρ₁) = 7800 kg/m³
density of material 2 (ρ₂) = 2700 kg/m³
volume fraction of material 1 (f₁) = 0.3
volume fraction of material 2 (f₂) = 0.7
average density = ρ₁×f₁ + ρ₂×f₂ = 7800×0.3 + 2700×0.7 = 4230 kg/m³

This shows different density values working together.

18. Angular Momentum Kind (NISTd60a)

Example: Conservation of angular momentum

initial angular momentum (L₁) = 50 kg·m²/s
moment of momentum (M) = L₁ = 50 kg·m²/s

This shows angular momentum and moment of momentum are equivalent.

19. Action Kind (NISTd60b)

Example: Angular impulse-momentum theorem

angular impulse (J) = 10 kg·m²/s
change in angular momentum (ΔL) = J = 10 kg·m²/s

This shows angular impulse and action working together.

20. Strain Kind (NISTd80c)

Example: Volume strain calculation

linear strain in x-direction (εₓ) = 0.02
linear strain in y-direction (εᵧ) = 0.02
linear strain in z-direction (εᵦ) = 0.02
volume strain (εᵥ) = εₓ + εᵧ + εᵦ + higher order terms ≈ 0.06

This shows how linear strains relate to volume strain.

21. Orientation Kind (NISTd80h)

Example: Angular measurement

rotation (θ) = 2 revolutions
angle per revolution = 2π radians
total angle = θ × 2π = 2 × 2π = 4π radians = 720 degrees

This shows rotation and angle working together.

22. Count Kind (NISTd80i)

Example: Statistical state calculation

number of entities (N) = 10²³
number of states per entity (s) = 5
total number of possible states = N × s = 10²³ × 5 = 5×10²³

This shows how number of entities and states work together.

23. Probability Kind (NISTd80j)

Example: Statistical mechanics calculation

statistical weight of state 1 (g₁) = 3
statistical weight of state 2 (g₂) = 1
probability of state 1 (p₁) = g₁/(g₁+g₂) = 3/(3+1) = 0.75
probability of state 2 (p₂) = g₂/(g₁+g₂) = 1/(3+1) = 0.25

This shows how probability and statistical weight work together.