Scientific Constants Guide: Nearly 2,000 Math and Science Constants

Calc Pro's Constants Calculator is a comprehensive reference library putting essential mathematical, physics, chemistry, and astronomical constants at your fingertips. No more searching textbooks or websites—every constant you need is just a tap away.

Overview

The Constants Calculator features:

• Nearly 2,000 constants in 9 categories
• Full precision values with units
• Easy insertion into calculations
• Comprehensive descriptions for each constant

Constant Categories

Constants are organized into nine top-level categories. Mathematics, Physics, Solar System and Elements are included free. Chemistry, Biology, Engineering, Computer Science and Earth Science unlock with Pro Premium in the iPhone & iPad app (see section 8). The Physics category is divided into groups such as Universal, Electromagnetic, Atomic and Nuclear, and Physico-chemical constants, covered in sections 2–5.

1. Mathematical Constants

These fundamental numbers appear throughout mathematics:

Constant	Symbol	Value	Description
Pi	π	3.14159265358979...	Ratio of circumference to diameter
Euler's number	e	2.71828182845904...	Base of natural logarithms
Golden ratio	φ	1.61803398874989...	(1 + √5) / 2
Square root of 2	√2	1.41421356237309...	Diagonal of unit square
Square root of 3	√3	1.73205080756887...	Height of equilateral triangle
Natural log of 2	ln(2)	0.69314718055994...	Time to double at 100% growth
Natural log of 10	ln(10)	2.30258509299404...	Conversion factor for logarithms
Euler-Mascheroni	γ	0.57721566490153...	Limit constant in harmonic series

2. Universal Physical Constants

Fundamental constants of nature:

Constant	Symbol	Value	Units
Speed of light	c	299,792,458	m/s
Gravitational constant	G	6.67430 × 10⁻¹¹	m³/(kg·s²)
Planck's constant	h	6.62607 × 10⁻³⁴	J·s
Reduced Planck	ℏ	1.05457 × 10⁻³⁴	J·s
Boltzmann constant	k	1.38065 × 10⁻²³	J/K
Stefan-Boltzmann	σ	5.67037 × 10⁻⁸	W/(m²·K⁴)
Vacuum permittivity	ε₀	8.85419 × 10⁻¹²	F/m
Vacuum permeability	μ₀	1.25664 × 10⁻⁶	H/m

3. Atomic & Nuclear Constants

For particle physics and chemistry:

Constant	Symbol	Value	Units
Elementary charge	e	1.60218 × 10⁻¹⁹	C
Electron mass	mₑ	9.10938 × 10⁻³¹	kg
Proton mass	mₚ	1.67262 × 10⁻²⁷	kg
Neutron mass	mₙ	1.67493 × 10⁻²⁷	kg
Atomic mass unit	u	1.66054 × 10⁻²⁷	kg
Avogadro's number	Nₐ	6.02214 × 10²³	mol⁻¹
Faraday constant	F	96485.33	C/mol
Rydberg constant	R∞	1.09737 × 10⁷	m⁻¹
Bohr radius	a₀	5.29177 × 10⁻¹¹	m
Fine structure	α	7.29735 × 10⁻³	(dimensionless)

4. Thermodynamic Constants

For heat and energy calculations:

Constant	Symbol	Value	Units
Gas constant	R	8.31446	J/(mol·K)
Boltzmann constant	k	1.38065 × 10⁻²³	J/K
Standard atmosphere	atm	101,325	Pa
Absolute zero	0 K	-273.15	°C
Triple point of water		273.16	K

5. Electromagnetic Constants

For electrical and magnetic calculations:

Constant	Symbol	Value	Units
Speed of light	c	299,792,458	m/s
Vacuum permittivity	ε₀	8.85419 × 10⁻¹²	F/m
Vacuum permeability	μ₀	1.25664 × 10⁻⁶	H/m
Impedance of vacuum	Z₀	376.730	Ω
Coulomb's constant	k	8.98755 × 10⁹	N·m²/C²

6. Solar System Data

Planetary and astronomical constants:

The Sun

Property	Value	Units
Mass	1.989 × 10³⁰	kg
Radius	696,340	km
Surface temperature	5,778	K
Luminosity	3.828 × 10²⁶	W

Earth

Property	Value	Units
Mass	5.972 × 10²⁴	kg
Mean radius	6,371	km
Equatorial radius	6,378	km
Polar radius	6,357	km
Surface gravity	9.807	m/s²
Escape velocity	11.186	km/s
Orbital period	365.256	days
Orbital velocity	29.78	km/s
Distance from Sun	149.6 × 10⁶	km

The Moon

Property	Value	Units
Mass	7.342 × 10²²	kg
Radius	1,737	km
Surface gravity	1.62	m/s²
Distance from Earth	384,400	km
Orbital period	27.32	days

Other Planets

Each planet includes:

• Mass
• Radius
• Surface gravity
• Distance from Sun
• Orbital period
• Number of moons

7. Chemical Elements

Reference data for the periodic table:

Element	Symbol	Atomic #	Atomic Mass
Hydrogen	H	1	1.008
Helium	He	2	4.003
Lithium	Li	3	6.941
Carbon	C	6	12.011
Nitrogen	N	7	14.007
Oxygen	O	8	15.999
Iron	Fe	26	55.845
Copper	Cu	29	63.546
Silver	Ag	47	107.868
Gold	Au	79	196.967
Uranium	U	92	238.029

All elements from 1-118 available

8. Specialist Categories — Pro Premium

Five more categories cover the constants students and professionals reach for outside physics:

Category	Example constants
Chemistry	Water molecular weight (18.01528 g/mol), glucose molecular weight (180.15588 g/mol), standard molar volume (22.414 L/mol)
Biology	Human genome base pairs (3.2 × 10⁹), neurons in the human brain (8.6 × 10¹⁰), blood pH (7.4)
Engineering	Density of steel (7,850 kg/m³), Young's modulus of steel (2.0 × 10¹¹ Pa), horsepower (745.7 W)
Computer Science	Kibibyte (1,024 bytes), max signed 32-bit integer (2,147,483,647), machine epsilon (2.22 × 10⁻¹⁶)
Earth Science	Astronomical unit (1.496 × 10¹¹ m), height of Mount Everest (8,848.86 m), age of Earth (4.543 × 10⁹ years)

How to Use Constants

Viewing a Constant

1. Open the Constants Calculator
2. Select a category (Math, Physics, etc.)
3. Browse or search for your constant
4. View the full-precision value and units

Using a Constant in Calculations

1. Find the constant you need
2. Tap to copy/insert the value
3. The value is inserted into your calculation

Example: Calculate Photon Energy

Calculate the energy of a photon with wavelength 500 nm:

E = hc/λ

1. Get Planck's constant (h): 6.62607 × 10⁻³⁴ J·s
2. Get speed of light (c): 299,792,458 m/s
3. Wavelength (λ): 500 × 10⁻⁹ m
4. Calculate: E = (6.626 × 10⁻³⁴)(3 × 10⁸) / (500 × 10⁻⁹)
5. Result: E ≈ 3.98 × 10⁻¹⁹ J

Practical Applications

Physics Problems

Calculate escape velocity:
v = √(2GM/r)

Using:

• G = 6.674 × 10⁻¹¹ m³/(kg·s²)
• M (Earth) = 5.972 × 10²⁴ kg
• r (Earth radius) = 6.371 × 10⁶ m

Result: v ≈ 11.2 km/s ✓

Chemistry Calculations

Molar mass calculations:

• Use atomic masses from elements table
• Water (H₂O): 2(1.008) + 15.999 = 18.015 g/mol

Avogadro calculations:

• Atoms in 12g of carbon = Nₐ = 6.022 × 10²³

Engineering Applications

Electrical calculations:

• Using ε₀ for capacitor design
• Using μ₀ for inductor calculations
• Using c for transmission line impedance

Thermal calculations:

• Stefan-Boltzmann law for radiation
• Boltzmann constant for energy per particle
• Gas constant for ideal gas law

Astronomy

Orbital calculations:

• Use planetary masses and distances
• Calculate orbital periods
• Determine gravitational forces

Example: Moon's orbital velocity
v = √(GM_Earth / r_orbit)
v = √(6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 3.844 × 10⁸)
v ≈ 1.02 km/s ✓

Categories Quick Reference

When to Use Each Category

If you need...	Use this category
π, e, φ	Mathematical
c, G, h	Universal Physical
mₑ, mₚ, Nₐ	Atomic & Nuclear
R, k, atm	Thermodynamic
ε₀, μ₀	Electromagnetic
Planet data	Solar System
Atomic masses	Chemical Elements
Molecular weights, molar volume	Chemistry (Pro Premium)
Genome, cell and body data	Biology (Pro Premium)
Material densities, moduli	Engineering (Pro Premium)
Byte sizes, integer limits	Computer Science (Pro Premium)
Earth and ocean data	Earth Science (Pro Premium)

Tips for Using Constants

1. Check Units

Always verify the units match your calculation system:

• SI units (meters, kilograms, seconds)
• CGS units (centimeters, grams, seconds)
• Imperial/US units

2. Use Scientific Notation

For very large or small constants, Calc Pro displays and handles scientific notation properly.

3. Significant Figures

Constants are provided to high precision. Round your final answer appropriately for your application.

4. Verify Critical Values

For important calculations, cross-reference with authoritative sources (NIST, CODATA).

5. Temperature Units

Be careful with temperature constants:

• Absolute zero: 0 K = -273.15°C = -459.67°F
• Always use Kelvin for physics calculations

Educational Value

For Students

• Quick reference during homework
• Learn relationships between constants
• Explore units and dimensional analysis
• Verify textbook values

For Teachers

• Classroom demonstrations
• Consistent reference values
• Show constant relationships

For Professionals

• Engineering calculations
• Research reference
• Quick verification
• Consistent precision

Fun Facts About Constants

Pi (π)

• Appears in circles, spheres, waves, and probability
• Calculated to trillions of digits
• March 14 is Pi Day (3/14)

Speed of Light (c)

• Exactly defined as 299,792,458 m/s
• Nothing with mass can reach it
• Foundation of special relativity

Avogadro's Number

• Named after Amedeo Avogadro
• Connects microscopic and macroscopic scales
• Used to define the mole

Golden Ratio (φ)

• Appears in art, architecture, and nature
• Fibonacci sequence ratios approach φ
• Found in spirals and proportions

Conclusion

Calc Pro's Constants Calculator transforms your device into a comprehensive scientific reference. Whether you're solving physics problems, performing chemistry calculations, or exploring astronomy, having precise constant values at your fingertips saves time and ensures accuracy.

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