Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit. Although the number of physical quantities appears to be very large, we need only a limited number of units for expressing all the physical quantities, since they are inter- related with one another. The units for the fundamental or base quantities are called fundamental or base units. The units of all other physical quantities can be expressed as combinations of the base units. Such units obtained for the derived quantities are called derived units. A complete set of these units, both the base units and derived units, is known as the system of units.
THE INTERNATIONAL SYSTEM OF UNITS
In earlier time scientists of different countries were using different systems of units for measurement. Three such systems, the CGS, the FPS (or British) system and the MKS system were in use extensively till recently. The base units for length, mass and time in these systems were as follows :
In CGS system they were centimetre, gram and second respectively.
In FPS system they were foot, pound and second respectively.
In MKS system they were metre, kilogram and second respectively.
CGS-FPS-MKS Unit Converter
Unit System Converter
CGS ↔ FPS ↔ MKS/SI Inter-conversion Simulator
CGS
Centimetre-Gram-Second
cm, g, s
FPS
Foot-Pound-Second
ft, lb, s
MKS
Metre-Kilogram-Second
m, kg, s (SI)
Length|[L]
🔄 Convert
⬇️
CGS
CGS System
1
cm
FPS
FPS System
1
ft
MKS
MKS/SI System
1
m
📊 Conversion Factors (Length)
From → To
CGS
FPS
MKS
📚 Base Unit Relationships
📏 Length
1 m= 100 cm
1 m= 3.281 ft
1 ft= 30.48 cm
⚖️ Mass
1 kg= 1000 g
1 kg= 2.205 lb
1 lb= 453.6 g
⏱️ Time
Second (s)Same in all
Time unit is identical across CGS, FPS, and MKS systems
🔬 Current Conversion Formula
1 m = 100 cm = 3.28084 ft
Length conversion between metre, centimetre, and foot
The system of units which is at present internationally accepted for measurement is the Système internationale d’ Unites (French for International System of Units), abbreviated as SI. The SI, with standard scheme of symbols, units and abbreviations, developed by the Bureau International des Poids et measures (The International Bureau of Weights and Measures, BIPM) in 1971 were recently revised by the General Conference on Weights and Measures in November 2018. The scheme is now for international usage in scientific, technical, industrial and commercial work. Because SI units used decimal system, conversions within the system are quite simple and convenient. We shall follow the SI units in this book. In SI, there are seven base units as given. Besides the seven base units, there are two more units that are defined for (a) plane angle dθ as the ratio of length of arc ds to the radius r and (b) solid angle dΩ as the ratio of the intercepted area dA of the spherical surface, described about the apex O as the Centre, to the square of its radius r, as shown. The unit for plane angle is radian with the symbol rad and the unit for the solid angle is steradian with the symbol sr. Both these are dimensionless quantities.
Length
SI Metre Definition Simulator
📏
The SI Definition of the Metre
Understanding how the metre is defined by the speed of light and caesium-133 atomic frequency
m
Official SI Definition (2019)
The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuumc to be 299,792,458 when expressed in the unit m·s⁻¹, where the second is defined in terms of the caesium frequency∆νCs.
💡Speed of Light (c)
299,792,458
m/s (exact)
⚛️Caesium-133 Frequency (∆νCs)
9,192,631,770
Hz (oscillations/second)
🚀 Speed of Light Visualization
0 m~75M m~150M m~225M m299,792,458 m
Light Photon
Travels 299,792,458 m in 1 second
⚡ Light travels approximately 7.5 times around Earth in one second
⚛️ Caesium-133 Atomic Clock
Cs133
Hyperfine Transition Frequency
The radiation emitted during the transition between two hyperfine levels of the caesium-133 ground state
Oscillations per second:
9,192,631,770
Hz (cycles/second)
Live Oscillation Counter
0
Simulating ~9.19 oscillations/second (10⁹× slower than real)
📐 The Mathematical Definition
1 metre = c × (1/∆νCs) × ∆νCs/c
1
Define the second using caesium
1 second = 9,192,631,770 oscillations of Cs-133
2
Fix the speed of light
c = 299,792,458 m/s (exact, by definition)
3
Derive the metre
1 metre = distance light travels in 1/299,792,458 second
Therefore:
1 m = c / 299,792,458 = distance light travels in ≈ 30.663319 Cs-133 oscillations
🧮 Interactive Calculator
Distance → Light Travel Time
Light travel time:
3.336 × 10⁻⁹ seconds
≈ 30.66 Cs oscillations
Time → Distance Light Travels
Distance traveled:
299,792,458 m
≈ 7.48 Earth circumferences
📜 Evolution of the Metre Definition
1793
1/10,000,000 of the distance from equator to North Pole
1889
International Prototype Metre bar (platinum-iridium)
1960
1,650,763.73 wavelengths of krypton-86 radiation
1983 → Present
Distance light travels in 1/299,792,458 second (linked to c and ∆νCs)
Mass
SI Kilogram Definition Simulator
⚖️
The SI Definition of the Kilogram
Understanding how the kilogram is defined by the Planck constant and quantum mechanics
kg
Official SI Definition (2019)
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constanth to be 6.62607015 × 10⁻³⁴ when expressed in the unit J·s, which is equal to kg·m²·s⁻¹, where the metre and second are defined in terms of c and ∆νCs.
✨Planck Constant (h)
6.62607015
× 10⁻³⁴ J·s (exact)
💡Speed of Light (c)
299,792,458
m/s (exact)
⚛️Caesium Frequency (∆νCs)
9,192,631,770
Hz (exact)
⚖️ Kibble Balance: Measuring Mass with Electricity
How the Kibble Balance Works
The Kibble balance (formerly watt balance) relates mechanical power to electrical power:
mgv = UI
Where m = mass, g = gravity, v = velocity, U = voltage, I = current
The Quantum Connection
Through the Josephson effect and quantum Hall effect, voltage and resistance can be measured in terms of h and e (elementary charge), linking mass directly to the Planck constant.
✨ The Planck Constant: Quantum of Action
Photon Energy Equation
E = hν
Energy = Planck constant × frequency
Photon Energy Calculator
Try: 5×10¹⁴ Hz (visible light)
Photon energy (E = hν):
3.313 × 10⁻¹⁹ J
≈ 2.07 eV
📐 The Mathematical Definition
1 kg = h / (6.62607015 × 10⁻³⁴m²·s⁻¹)
Understanding the Units
J·s=kg·m²·s⁻¹
Joule-second = kilogram × metre² × per second
1
Define the second using caesium
1 s = 9,192,631,770 periods of Cs-133 radiation
2
Define the metre using speed of light
1 m = distance light travels in 1/299,792,458 s
3
Fix the Planck constant
h = 6.62607015 × 10⁻³⁴ J·s (exact, by definition)
4
Derive the kilogram
1 kg = h / (6.62607015 × 10⁻³⁴ m²·s⁻¹)
🧮 Mass-Energy Calculator
Mass → Rest Energy (E = mc²)
Rest energy:
8.988 × 10¹⁶ J
≈ 21.5 megatons TNT
Photons in 1 kg of Light
550 nm = green light
Number of photons:
2.49 × 10³⁵
Each: 3.61 × 10⁻¹⁹ J
📜 Evolution of the Kilogram Definition
1795
Mass of 1 litre of water at 4°C (the "grave")
1889
International Prototype Kilogram (IPK) - platinum-iridium cylinder in Paris
Problem Discovered
IPK drifting relative to copies - gained ~50 µg over 100 years
2019 → Present
Defined by fixing the Planck constant h = 6.62607015 × 10⁻³⁴ J·s
❓ Why the Planck Constant?
🌍 Universal
The Planck constant is a fundamental constant of nature - the same everywhere in the universe.
🔬 Measurable
Can be measured precisely using Kibble balances and quantum electrical standards.
♾️ Unchanging
Unlike a physical artifact, h doesn't drift, corrode, or change over time.
Second
SI Second Definition Simulator
⏱️
The SI Definition of the Second
Understanding how the second is defined by the caesium-133 atomic frequency
s
Official SI Definition (2019)
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9,192,631,770 when expressed in the unit Hz, which is equal to s⁻¹.
⚛️Caesium-133 Hyperfine Transition Frequency
9,192,631,770
Hz (oscillations per second) — exact by definition
⚛️ Caesium-133 Atom: The Time Standard
Cs133
What is the Hyperfine Transition?
The outermost electron of caesium-133 can exist in two slightly different energy states (spin orientations relative to the nucleus). When it transitions between these states, it emits or absorbs microwave radiation at exactly 9,192,631,770 Hz.
Why Caesium-133?
✓Only stable isotope of caesium
✓Single valence electron (simple structure)
✓Large hyperfine splitting (easy to measure)
✓Unaffected by magnetic fields (when shielded)
📊 Live Oscillation Counter
Oscillations Counted
0
Progress to 1 second0%
Simulated Seconds Elapsed
0.000
Microwave Frequency Visualization
Frequency: 9.192631770 GHz
Wavelength: ~3.26 cm (microwave)
⚡ Counter runs at ~9.19 oscillations/display-second (10⁹× slower than reality for visualization)
⚙️ How Atomic Clocks Work
1
Heat Caesium Atoms
Caesium is heated in an oven to create a beam of atoms traveling through a vacuum chamber.
2
Expose to Microwave Radiation
Atoms pass through a cavity filled with microwave radiation near 9,192,631,770 Hz.
3
Detect State Changes
When the frequency exactly matches, maximum atoms transition between hyperfine states.
4
Feedback Loop
The microwave frequency is continuously adjusted to maximize transitions, locking to atomic resonance.
Ephemeris second: based on Earth's orbital motion around the Sun
1967
First atomic definition using caesium-133 (same value used today)
2019 → Present
Reaffirmed with explicit frequency value: ∆νCs = 9,192,631,770 Hz (exact)
🎯 Precision & Applications
🛰️
GPS Navigation
Requires nanosecond precision for meter-level accuracy
📡
Telecommunications
Network synchronization across the globe
🔬
Scientific Research
Testing fundamental physics theories
💹
Financial Trading
High-frequency trading timestamps
Modern Caesium Clock Accuracy
± 1 second in 300 million years
Optical lattice clocks can achieve ± 1 second in 15 billion years!
Ampere
SI Ampere Definition Simulator
⚡
The SI Definition of the Ampere
Understanding how the ampere is defined by the elementary charge of electrons
A
Official SI Definition (2019)
The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary chargee to be 1.602176634 × 10⁻¹⁹ when expressed in the unit C (coulomb), which is equal to A·s, where the second is defined in terms of ∆νCs.
⚛️Elementary Charge (e)
1.602176634
× 10⁻¹⁹ C (exact by definition)
⚡1 Ampere Means
6.241509074 × 10¹⁸
electrons per second
🔌 Electric Current: Electrons in Motion
Current (I)
e⁻ = electron (negative charge)
What is Electric Current?
Electric current is the flow of electric charge. In metals, this is primarily the movement of electrons through a conductor. The ampere measures how much charge passes a point per second.
The Key Equation
I = Q / t
Current = Charge ÷ Time | 1 A = 1 C/s
⚛️ The Elementary Charge: Nature's Quantum of Electricity
+
Proton: +e
Electron: −e
|e| = 1.602176634 × 10⁻¹⁹ C
Why "Elementary"?
The elementary charge is the smallest unit of free electric charge observed in nature. All observable charges are integer multiples of this value. Quarks have fractional charges but are never observed in isolation.
Proton
+e
positive charge
Electron
−e
negative charge
Charge Conservation
Electric charge is always conserved. It cannot be created or destroyed, only transferred between objects.
📊 Live Current Simulator
Current Setting
1.00 A
0.1 A10 A
Electrons Passing Per Second
6.241509074 × 10¹⁸
Charge accumulated0.00 C
1 coulomb = 1 ampere × 1 second
Ammeter
Ammeter measures current flow through a circuit
🧮 Current & Charge Calculators
Electrons/second → Current
Electric current:
1.000000000 A
= 1 ampere
Charge → Number of Electrons
Number of electrons:
6.241509074 × 10¹⁸
≈ 6.24 quintillion
💡
LED Light
~20 mA
📱
Phone Charging
~2 A
🔌
Hair Dryer
~10 A
⚡
Lightning Bolt
~30,000 A
📐 The Mathematical Definition
1 A = 1 C / 1 s = e × 6.241509074×10¹⁸ / s
How the Units Connect
edefinesCand withsgivesA
1
Second is defined by caesium
1 s = 9,192,631,770 periods of Cs-133 hyperfine transition
2
Elementary charge is fixed
e = 1.602176634 × 10⁻¹⁹ C (exact, by definition)
3
Coulomb is derived
1 C = e × 6.241509074×10¹⁸ (charge of ~6.24 quintillion electrons)
4
Ampere is defined
1 A = 1 coulomb of charge flowing per second
📜 Evolution of the Ampere
1881
Named after André-Marie Ampère; defined by electrochemical deposition
1948
Defined by force between two parallel conductors (2×10⁻⁷ N/m at 1m apart)
Problem Identified
Force definition was impractical to realize with high precision
2019 → Present
Defined by fixing elementary charge e = 1.602176634 × 10⁻¹⁹ C (exact)
❓ Why the Elementary Charge?
⚛️ Fundamental
The elementary charge is a fundamental constant of nature — the basic unit of electric charge in the universe.
🔬 Measurable
Can be measured precisely using single-electron counting techniques and quantum electrical standards.
🔗 Connects to h
Together with Planck constant h, enables precise quantum electrical measurements via Josephson and quantum Hall effects.
Kelvin
SI Kelvin Definition Simulator
🌡️
The SI Definition of the Kelvin
Understanding how the kelvin is defined by the Boltzmann constant
K
Official SI Definition (2019)
The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constantk to be 1.380649 × 10⁻²³ when expressed in the unit J·K⁻¹.
⚛️Boltzmann Constant (k)
1.380649 × 10⁻²³
J/K (joules per kelvin) — exact by definition
⚛️ Temperature = Molecular Motion
Temperature: 300 K
Avg KE: 6.21 × 10⁻²¹ J
What is Temperature Really?
Temperature is a measure of the average kinetic energy of particles in a substance. Faster-moving molecules = higher temperature.
The Key Equation
Eavg = ³⁄₂ kT
Average kinetic energy = ³⁄₂ × Boltzmann constant × Temperature
50 K (Cold)1000 K (Hot)
🔬 The Boltzmann Constant: Bridge Between Scales
🔬
Microscopic World
Energy of single molecules
~10⁻²¹ joules
k
Boltzmann
Constant
🌡️
Macroscopic World
Temperature we can measure
~300 kelvin
Think of it this way:
The Boltzmann constant k = 1.380649 × 10⁻²³ J/K tells us: Each kelvin of temperature corresponds to about 1.38 × 10⁻²³ joules of thermal energy per particle.
📊 Interactive Temperature Converter
300 K
SI unit • Absolute zero = 0 K
K = °C + 273.15
K = (°F + 459.67) × 5/9
Thermal Energy per Particle
6.21 × 10⁻²¹ J
E = ³⁄₂ kT (for ideal gas)
🌡️ Temperature Reference Points
0 K1500 K
❄️
Absolute Zero
0 K
-273.15°C
🌌
Cosmic Background
2.7 K
-270.45°C
🧊
Water Freezes
273.15 K
0°C
🌡️
Room Temp
~300 K
~27°C
💨
Water Boils
373.15 K
100°C
☀️
Sun's Surface
5778 K
5505°C
🔗 How the Kelvin Connects to Fundamental Constants
k = 1.380649×10⁻²³ J·K⁻¹ = kg·m²·s⁻²·K⁻¹
∆νCsCaesium→ s
+
cLight speed→ m
+
hPlanck→ kg
+
kBoltzmann→ K
The kelvin is defined so that the Boltzmann constant has an exact fixed value, linking temperature to energy through fundamental physics constants.
📜 Evolution of the Kelvin
1848
Lord Kelvin proposes absolute temperature scale
1954
Kelvin defined as 1/273.16 of the triple point of water
Problem
Water-based definition limited by isotopic composition variations
2019 → Present
Defined by fixing k = 1.380649 × 10⁻²³ J/K (exact)
❓ Why the Boltzmann Constant?
⚛️ Fundamental
Links the microscopic world of atoms to macroscopic thermodynamics.
🎯 Universal
Same value everywhere in the universe, unlike water which varies.
📐 Measurable
Can be determined precisely using acoustic thermometry.
Mole
SI Mole Definition Simulator
⚛️
🔬
⚛️
🧪
⚛️
🧪
The SI Definition of the Mole
Understanding how the mole is defined by the Avogadro constant
mol
Official SI Definition (2019)
The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076 × 10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol⁻¹ and is called the Avogadro number.
⚛️Avogadro Constant (NA)
6.02214076 × 10²³
mol⁻¹ (per mole) — exact by definition
⚛️ Visualizing the Mole: Counting Particles
Particles shown: 16
1 mole = 6.022 × 10²³
Each dot represents ~10²² atoms!
How Big is Avogadro's Number?
If you counted 1 million particles per second, it would take you 19 trillion years to count one mole of particles — that's about 1,400 times the age of the universe!
The Key Equation
N = n × NA
Number of particles = Amount (moles) × Avogadro constant
mol
Number of particles:
6.02214076 × 10²³
🔬 What Can Be an "Elementary Entity"?
An elementary entity may be an atom, a molecule, an ion, an electron, any other particle, or a specified group of particles. The entity must always be specified!
⚛️
Atoms
e.g., Fe, C, O
🔗
Molecules
e.g., H₂O, CO₂
⚡
Ions
e.g., Na⁺, Cl⁻
⊖
Electrons
e⁻
◉
Photons
γ
🧬
Formula Units
e.g., NaCl
⚠️
Important!
Always specify the entity! "1 mole of oxygen" is ambiguous — is it O atoms or O₂ molecules? 1 mol O = 6.022×10²³ atoms, but 1 mol O₂ = 6.022×10²³ molecules (= 1.204×10²⁴ atoms).
⚖️ The Mole-Mass Connection
⚛️
Atomic Scale
Individual atoms/molecules
measured in u (daltons)
NA
Avogadro
Constant
⚖️
Lab Scale
Weighable amounts
measured in grams
The Magic Relationship
M (g/mol) ≈ Ar (atomic mass)
The molar mass in g/mol numerically equals the atomic/molecular mass in u
📊 What Does One Mole Look Like?
💧
Water (H₂O)
18.015 g/mol
~18 mL of water (about 1 tablespoon)
⬛
Carbon (C)
12.011 g/mol
~12 g of graphite (pencil lead)
🥇
Gold (Au)
196.97 g/mol
~197 g cube (2.3 cm sides)
🧂
Salt (NaCl)
58.44 g/mol
~58 g (about 3 tablespoons)
Each of these amounts contains exactly 6.02214076 × 10²³ of their respective entities!
🔗 How the Mole Connects to the SI System
NA = 6.02214076 × 10²³ mol-1 — exact by definition
n
Amount
(mol)
×
NA
Avogadro
(mol⁻¹)
=
N
Number
(particles)
Key insight:
The mole is now defined by fixing NA to an exact value, rather than being tied to any physical artifact (like ¹²C was before 2019). This makes it universal and unchanging.
📜 Evolution of the Mole
1811
Avogadro proposes equal volumes of gases contain equal numbers of particles
1909
Jean Perrin determines Avogadro's number experimentally using Brownian motion
1971
Mole becomes SI base unit, defined as atoms in 12 g of carbon-12
Problem
Carbon-12 definition tied mole to kilogram, which had its own instability issues
2019 → Present
Defined by fixing NA = 6.02214076 × 10²³ mol⁻¹ (exact), independent of any material
❓ Why Fix the Avogadro Constant?
🎯 Exact & Unchanging
By fixing NA exactly, the mole is no longer dependent on any physical artifact that could change.
🔓 Independent
The mole is now independent of the kilogram definition, making both units more robust.
🌍 Universal
Anyone, anywhere can realize the mole from the definition without needing a reference sample.
🤯 Mind-Blowing Mole Facts
🌊 Ocean of Particles
A mole of water drops would fill all the world's oceans about 300 million times over.
⏰ Counting Forever
At 1 billion counts per second, counting to NA would take about 19 million billion years.
🎾 Tennis Ball Earth
A mole of tennis balls would cover the Earth's surface to a depth of about 60 km.
💨 Air We Breathe
Every breath you take contains about 10²² molecules — roughly 0.02 moles of air.
Candla
SI Candela Definition Simulator
💡
The SI Definition of the Candela
Understanding how the candela is defined by luminous efficacy
cd
Official SI Definition (2019)
The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, Kcd, to be 683 when expressed in the unit lm·W⁻¹.
✨Luminous Efficacy Constant (Kcd)
683 lm/W
at 540 THz (555 nm green light) — exact by definition
💡 Visualizing Luminous Intensity
Luminous Intensity: 100 cd
Direction: ↓ Forward
What is Luminous Intensity?
Luminous intensity measures how much visible light is emitted in a specific direction. Unlike total light output (lumens), candelas measure light "per unit solid angle" — how concentrated the beam is.
The Key Relationships
Iv (cd) = Φv (lm) / Ω (sr)
Luminous intensity = Luminous flux / Solid angle
1 cd (candle)500 cd (bright LED)
👁️ Why 540 THz? The Peak of Human Vision
Visible Light Spectrum (380–700 nm)
555 nm
380 nm (Violet)555 nm (Green)700 nm (Red)
👁️ Peak Sensitivity
The human eye is most sensitive to yellow-green light at exactly 555 nm (540 THz). This is where we perceive the most brightness per watt of light power.
⚡ Luminous Efficacy
At 555 nm, 683 lumens of perceived brightness are produced per watt of radiant power. Other wavelengths produce fewer lumens per watt because our eyes are less sensitive to them.
The Frequency-Wavelength Relationship
f = 540 × 10¹² Hz ↔λ = c/f ≈ 555 nm
The SI definition uses frequency (540 THz) because it's independent of the medium
🔬 Understanding the Units
💡
Candela
cd
Luminous intensity
✨
Lumen
lm
Luminous flux (cd·sr)
📐
Steradian
sr
Solid angle
⚡
Watt
W
Radiant power
Kcd = 683 lm·W⁻¹ = 683 cd·sr·W⁻¹
In base SI units:
Kcd = 683 cd·sr·kg⁻¹·m⁻²·s³
Where kg, m, and s are defined by h, c, and ΔνCs
📐 What is a Solid Angle? Understanding Steradians
Steradian Definition
A steradian is the 3D equivalent of a radian. It's the solid angle that cuts out an area equal to r² on a sphere of radius r.
Full Sphere
Full sphere = 4π sr ≈ 12.57 sr
A light source emitting uniformly in all directions spreads its lumens across 4π steradians.
Why It Matters
The candela measures light per steradian, telling us how concentrated the light is in a particular direction, not just total output.
⚖️ Luminous vs. Radiant: What's the Difference?
📡
Radiant (Physical)
Total electromagnetic power
Watts (W)
V(λ)
Eye Response
Function
👁️
Luminous (Perceptual)
Brightness as humans see it
Lumens (lm), Candelas (cd)
The conversion:
Luminous quantities weight radiant quantities by how sensitive our eyes are at each wavelength. Infrared and ultraviolet carry energy but produce zero lumens because we can't see them!
🌟 Real-World Luminous Intensities
🕯️
Candle
~1 cd
Original standard
📱
Phone Screen
~500 cd/m²
(luminance)
💡
LED Bulb
~70 cd
60W equivalent
🔦
Flashlight
~10,000 cd
focused beam
🚗
Car Headlight
~20,000 cd
high beam
🔍
Lighthouse
~200,000 cd
intense beam
💡 Fun fact: The word "candela" literally means "candle" in Latin — the original unit was based on the light from a standard candle!
📜 Evolution of Light Measurement
1860s
Standard candles used — literally burning candles with specific wax composition
1948
"New candle" defined using blackbody radiation at platinum's freezing point (2042 K)
1979
Candela redefined using monochromatic 555 nm light and Kcd = 683 lm/W
2019 → Present
Kcd = 683 fixed as exact, frequency specified as 540 × 10¹² Hz exactly
🔗 How the Candela Connects to Other SI Units
ΔνCsCaesium→ s
+
cLight speed→ m
+
hPlanck→ kg
+
KcdLum. Efficacy→ cd
The candela is defined so that Kcd has an exact fixed value, linking human light perception to the physical unit of power (watts).
❓ Why Define the Candela This Way?
👁️ Human-Centered
Unlike other SI units, the candela is about perceived light — it's defined to match human vision at its most sensitive wavelength.
🎯 Practical
Essential for lighting design, display technology, photography, and any field where human perception of brightness matters.
🔬 Reproducible
By fixing Kcd exactly, any lab can realize the candela without needing a physical reference artifact.
