Datasets:
RANDMEDIATION
/
PhysicsBabel

Dataset card Data Studio Files
xet
 Community
1
size
int64
2
8
keys
stringlengths
10
106
symbols
stringlengths
3
29
domains
stringclasses
62 values
pi
stringlengths
3
46
equation
stringlengths
10
59
name
stringclasses
19 values
n_const
int64
0
4
n_domains
int64
1
6
max_exp
int64
1
34
exp_l1
int64
2
134
complexity
float64
0
113
score
float64
-104.8
10
plausible
bool
2 classes
exponents
stringlengths
27
177
5
acceleration,conductivity,length,mass,voltage
m·ℓ·a·U·σ
em,mechanics
m²·ℓ⁻¹·a³·U⁻⁴·σ⁻²
ℓ = k₀ · m²·a³·U⁻⁴·σ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "-1", "acceleration": "3", "voltage": "-4", "conductivity": "-2"}
5
acceleration,length,mass,resistivity,voltage
m·ℓ·a·U·ρ_e
em,mechanics
m²·ℓ⁻¹·a³·U⁻⁴·ρ_e²
ℓ = k₀ · m²·a³·U⁻⁴·ρ_e²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "-1", "acceleration": "3", "voltage": "-4", "resistivity": "2"}
5
acceleration,elem_charge,length,mass,voltage
m·ℓ·a·U·e
constants,em,mechanics
m·ℓ·a·U⁻¹·e⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·U·e
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "acceleration": "1", "voltage": "-1", "elem_charge": "-1"}
5
acceleration,efield,length,mass,resistance
m·ℓ·a·R·E_f
em,mechanics
m²·ℓ⁻³·a³·R²·E_f⁻⁴
m = k₀ · ℓ³ᐟ²·a⁻³ᐟ²·R⁻¹·E_f²
null
0
2
4
14
11.4
-1.9
false
{"mass": "2", "length": "-3", "acceleration": "3", "resistance": "2", "efield": "-4"}
5
acceleration,bfield,length,mass,resistance
m·ℓ·a·R·B
em,mechanics
m²·ℓ⁻⁵·a·R²·B⁻⁴
a = k₀ · m⁻²·ℓ⁵·R⁻²·B⁴
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "-5", "acceleration": "1", "resistance": "2", "bfield": "-4"}
5
acceleration,length,mag_flux,mass,resistance
m·ℓ·a·R·Φ
em,mechanics
m²·ℓ³·a·R²·Φ⁻⁴
a = k₀ · m⁻²·ℓ⁻³·R⁻²·Φ⁴
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "3", "acceleration": "1", "resistance": "2", "mag_flux": "-4"}
5
acceleration,elem_charge,length,mass,resistance
m·ℓ·a·R·e
constants,em,mechanics
m²·ℓ³·a·R⁻²·e⁻⁴
a = k₀ · m⁻²·ℓ⁻³·R²·e⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "2", "length": "3", "acceleration": "1", "resistance": "-2", "elem_charge": "-4"}
5
acceleration,capacitance,efield,length,mass
m·ℓ·a·C_e·E_f
em,mechanics
m·ℓ⁻¹·a·C_e⁻¹·E_f⁻²
m = k₀ · ℓ·a⁻¹·C_e·E_f²
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-1", "acceleration": "1", "capacitance": "-1", "efield": "-2"}
5
acceleration,capacitance,elem_charge,length,mass
m·ℓ·a·C_e·e
constants,em,mechanics
m·ℓ·a·C_e·e⁻²
m = k₀ · ℓ⁻¹·a⁻¹·C_e⁻¹·e²
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "1", "acceleration": "1", "capacitance": "1", "elem_charge": "-2"}
5
acceleration,efield,inductance,length,mass
m·ℓ·a·L_e·E_f
em,mechanics
m·ℓ⁻²·a²·L_e·E_f⁻²
m = k₀ · ℓ²·a⁻²·L_e⁻¹·E_f²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "acceleration": "2", "inductance": "1", "efield": "-2"}
5
acceleration,bfield,inductance,length,mass
m·ℓ·a·L_e·B
em,mechanics
m·ℓ⁻³·a·L_e·B⁻²
m = k₀ · ℓ³·a⁻¹·L_e⁻¹·B²
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-3", "acceleration": "1", "inductance": "1", "bfield": "-2"}
5
acceleration,inductance,length,mag_flux,mass
m·ℓ·a·L_e·Φ
em,mechanics
m·ℓ·a·L_e·Φ⁻²
m = k₀ · ℓ⁻¹·a⁻¹·L_e⁻¹·Φ²
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "acceleration": "1", "inductance": "1", "mag_flux": "-2"}
5
acceleration,efield,length,mass,permittivity
m·ℓ·a·E_f·ε
em,mechanics
m·ℓ⁻²·a·E_f⁻²·ε⁻¹
m = k₀ · ℓ²·a⁻¹·E_f²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "acceleration": "1", "efield": "-2", "permittivity": "-1"}
5
acceleration,efield,length,mass,permeability
m·ℓ·a·E_f·μ₀
em,mechanics
m·ℓ⁻¹·a²·E_f⁻²·μ₀
m = k₀ · ℓ·a⁻²·E_f²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-1", "acceleration": "2", "efield": "-2", "permeability": "1"}
5
acceleration,conductivity,efield,length,mass
m·ℓ·a·E_f·σ
em,mechanics
m²·ℓ⁻⁵·a³·E_f⁻⁴·σ⁻²
m = k₀ · ℓ⁵ᐟ²·a⁻³ᐟ²·E_f²·σ
null
0
2
5
16
13.3
-3.8
false
{"mass": "2", "length": "-5", "acceleration": "3", "efield": "-4", "conductivity": "-2"}
5
acceleration,efield,length,mass,resistivity
m·ℓ·a·E_f·ρ_e
em,mechanics
m²·ℓ⁻⁵·a³·E_f⁻⁴·ρ_e²
m = k₀ · ℓ⁵ᐟ²·a⁻³ᐟ²·E_f²·ρ_e⁻¹
null
0
2
5
16
13.3
-3.8
false
{"mass": "2", "length": "-5", "acceleration": "3", "efield": "-4", "resistivity": "2"}
5
acceleration,bfield,length,mass,permeability
m·ℓ·a·B·μ₀
em,mechanics
m·ℓ⁻²·a·B⁻²·μ₀
m = k₀ · ℓ²·a⁻¹·B²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "acceleration": "1", "bfield": "-2", "permeability": "1"}
5
acceleration,bfield,conductivity,length,mass
m·ℓ·a·B·σ
em,mechanics
m²·ℓ⁻⁷·a·B⁻⁴·σ⁻²
a = k₀ · m⁻²·ℓ⁷·B⁴·σ²
null
0
2
7
16
14.3
-4.8
false
{"mass": "2", "length": "-7", "acceleration": "1", "bfield": "-4", "conductivity": "-2"}
5
acceleration,bfield,length,mass,resistivity
m·ℓ·a·B·ρ_e
em,mechanics
m²·ℓ⁻⁷·a·B⁻⁴·ρ_e²
a = k₀ · m⁻²·ℓ⁷·B⁴·ρ_e⁻²
null
0
2
7
16
14.3
-4.8
false
{"mass": "2", "length": "-7", "acceleration": "1", "bfield": "-4", "resistivity": "2"}
5
acceleration,bfield,elem_charge,length,mass
m·ℓ·a·B·e
constants,em,mechanics
m²·ℓ⁻¹·a·B⁻²·e⁻²
ℓ = k₀ · m²·a·B⁻²·e⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "2", "length": "-1", "acceleration": "1", "bfield": "-2", "elem_charge": "-2"}
5
acceleration,length,mag_flux,mass,permeability
m·ℓ·a·Φ·μ₀
em,mechanics
m·ℓ²·a·Φ⁻²·μ₀
m = k₀ · ℓ⁻²·a⁻¹·Φ²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "acceleration": "1", "mag_flux": "-2", "permeability": "1"}
5
acceleration,conductivity,length,mag_flux,mass
m·ℓ·a·Φ·σ
em,mechanics
m²·ℓ·a·Φ⁻⁴·σ⁻²
ℓ = k₀ · m⁻²·a⁻¹·Φ⁴·σ²
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "length": "1", "acceleration": "1", "mag_flux": "-4", "conductivity": "-2"}
5
acceleration,length,mag_flux,mass,resistivity
m·ℓ·a·Φ·ρ_e
em,mechanics
m²·ℓ·a·Φ⁻⁴·ρ_e²
ℓ = k₀ · m⁻²·a⁻¹·Φ⁴·ρ_e⁻²
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "length": "1", "acceleration": "1", "mag_flux": "-4", "resistivity": "2"}
5
acceleration,elem_charge,length,mag_flux,mass
m·ℓ·a·Φ·e
constants,em,mechanics
m²·ℓ³·a·Φ⁻²·e⁻²
a = k₀ · m⁻²·ℓ⁻³·Φ²·e²
null
1
3
3
10
8.7
0.3
false
{"mass": "2", "length": "3", "acceleration": "1", "mag_flux": "-2", "elem_charge": "-2"}
5
acceleration,elem_charge,length,mass,permittivity
m·ℓ·a·ε·e
constants,em,mechanics
m·ℓ²·a·ε·e⁻²
m = k₀ · ℓ⁻²·a⁻¹·ε⁻¹·e²
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "length": "2", "acceleration": "1", "permittivity": "1", "elem_charge": "-2"}
5
acceleration,conductivity,elem_charge,length,mass
m·ℓ·a·σ·e
constants,em,mechanics
m²·ℓ⁵·a·σ²·e⁻⁴
a = k₀ · m⁻²·ℓ⁻⁵·σ⁻²·e⁴
null
1
3
5
14
12.5
-3.5
false
{"mass": "2", "length": "5", "acceleration": "1", "conductivity": "2", "elem_charge": "-4"}
5
acceleration,elem_charge,length,mass,resistivity
m·ℓ·a·ρ_e·e
constants,em,mechanics
m²·ℓ⁵·a·ρ_e⁻²·e⁻⁴
a = k₀ · m⁻²·ℓ⁻⁵·ρ_e²·e⁴
null
1
3
5
14
12.5
-3.5
false
{"mass": "2", "length": "5", "acceleration": "1", "resistivity": "-2", "elem_charge": "-4"}
5
acceleration,amount,length,mass,molar_energy
m·ℓ·a·n·E_m
chemistry,mechanics
m·ℓ·a·n⁻¹·E_m⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·n·E_m
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "acceleration": "1", "amount": "-1", "molar_energy": "-1"}
5
acceleration,cat_activity,length,mass,molar_mass
m·ℓ·a·M_m·z
chemistry,mechanics
m²·ℓ⁻¹·a·M_m⁻²·z⁻²
ℓ = k₀ · m²·a·M_m⁻²·z⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "length": "-1", "acceleration": "1", "molar_mass": "-2", "cat_activity": "-2"}
5
acceleration,concentration,length,mass,molar_energy
m·ℓ·a·c_n·E_m
chemistry,mechanics
m·ℓ⁻²·a·c_n⁻¹·E_m⁻¹
m = k₀ · ℓ²·a⁻¹·c_n·E_m
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-2", "acceleration": "1", "concentration": "-1", "molar_energy": "-1"}
6
acceleration,boltzmann,gas_constant,length,mass,molar_energy
m·ℓ·a·E_m·R·k_B
chemistry,constants,mechanics
m·ℓ·a·E_m⁻¹·R·k_B⁻¹
m = k₀ · ℓ⁻¹·a⁻¹·E_m·R⁻¹·k_B
null
1
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "acceleration": "1", "molar_energy": "-1", "gas_constant": "1", "boltzmann": "-1"}
5
acceleration,cat_activity,length,mass,molar_energy
m·ℓ·a·E_m·z
chemistry,mechanics
m²·ℓ·a³·E_m⁻²·z⁻²
ℓ = k₀ · m⁻²·a⁻³·E_m²·z²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "1", "acceleration": "3", "molar_energy": "-2", "cat_activity": "-2"}
5
acceleration,avogadro,length,mass,molar_energy
m·ℓ·a·E_m·N_A
chemistry,constants,mechanics
m·ℓ·a·E_m⁻¹·N_A
m = k₀ · ℓ⁻¹·a⁻¹·E_m·N_A⁻¹
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "acceleration": "1", "molar_energy": "-1", "avogadro": "1"}
4
acceleration,grav_const,length,mass
m·ℓ·a·G
constants,mechanics
m·ℓ⁻²·a⁻¹·G
m = k₀ · ℓ²·a·G⁻¹
null
1
2
2
5
3.8
5.7
true
{"mass": "1", "length": "-2", "acceleration": "-1", "grav_const": "1"}
4
acceleration,length,mass,planck
m·ℓ·a·h
constants,mechanics
m²·ℓ³·a·h⁻²
a = k₀ · m⁻²·ℓ⁻³·h²
null
1
2
3
8
6.4
3.1
true
{"mass": "2", "length": "3", "acceleration": "1", "planck": "-2"}
4
energy,gravity,length,mass
m·ℓ·g·E
mechanics
m·ℓ·g·E⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·E
null
0
1
1
4
2
8
true
{"mass": "1", "length": "1", "gravity": "1", "energy": "-1"}
4
gravity,length,mass,torque
m·ℓ·g·τ
mechanics
m·ℓ·g·τ⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·τ
null
0
1
1
4
2
8
true
{"mass": "1", "length": "1", "gravity": "1", "torque": "-1"}
4
gravity,length,mass,power
m·ℓ·g·P
mechanics
m²·ℓ·g³·P⁻²
ℓ = k₀ · m⁻²·g⁻³·P²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "1", "gravity": "3", "power": "-2"}
4
gravity,length,mass,momentum
m·ℓ·g·p
mechanics
m²·ℓ·g·p⁻²
ℓ = k₀ · m⁻²·g⁻¹·p²
null
0
1
2
6
3.9
6.1
true
{"mass": "2", "length": "1", "gravity": "1", "momentum": "-2"}
4
ang_momentum,gravity,length,mass
m·ℓ·g·Lₐ
mechanics
m²·ℓ³·g·Lₐ⁻²
g = k₀ · m⁻²·ℓ⁻³·Lₐ²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "3", "gravity": "1", "ang_momentum": "-2"}
4
action,gravity,length,mass
m·ℓ·g·S
mechanics
m²·ℓ³·g·S⁻²
g = k₀ · m⁻²·ℓ⁻³·S²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "3", "gravity": "1", "action": "-2"}
4
gravity,length,mass,pressure
m·ℓ·g·P_p
mechanics
m·ℓ⁻²·g·P_p⁻¹
m = k₀ · ℓ²·g⁻¹·P_p
null
0
1
2
5
3.2
6.8
true
{"mass": "1", "length": "-2", "gravity": "1", "pressure": "-1"}
4
gravity,length,mass,viscosity
m·ℓ·g·μ
mechanics
m²·ℓ⁻³·g·μ⁻²
g = k₀ · m⁻²·ℓ³·μ²
null
0
1
3
8
5.8
4.2
true
{"mass": "2", "length": "-3", "gravity": "1", "viscosity": "-2"}
4
gravity,length,mass,stiffness
m·ℓ·g·k
mechanics
m·ℓ⁻¹·g·k⁻¹
m = k₀ · ℓ·g⁻¹·k
null
0
1
1
4
2
8
true
{"mass": "1", "length": "-1", "gravity": "1", "stiffness": "-1"}
4
gravity,length,mass,surf_tension
m·ℓ·g·γ
mechanics
m·ℓ⁻¹·g·γ⁻¹
m = k₀ · ℓ·g⁻¹·γ
null
0
1
1
4
2
8
true
{"mass": "1", "length": "-1", "gravity": "1", "surf_tension": "-1"}
5
entropy,gravity,length,mass,temperature
m·ℓ·g·Θ·S_e
mechanics,thermo
m·ℓ·g·Θ⁻¹·S_e⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·Θ·S_e
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "gravity": "1", "temperature": "-1", "entropy": "-1"}
5
gravity,heat_capacity,length,mass,temperature
m·ℓ·g·Θ·C
mechanics,thermo
m·ℓ·g·Θ⁻¹·C⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·Θ·C
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "gravity": "1", "temperature": "-1", "heat_capacity": "-1"}
5
gravity,length,mass,temperature,thermal_cond
m·ℓ·g·Θ·κ
mechanics,thermo
m²·ℓ⁻¹·g³·Θ⁻²·κ⁻²
ℓ = k₀ · m²·g³·Θ⁻²·κ⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-1", "gravity": "3", "temperature": "-2", "thermal_cond": "-2"}
6
amount,gas_constant,gravity,length,mass,temperature
m·ℓ·g·Θ·n·R
chemistry,mechanics,thermo
m·ℓ·g·Θ⁻¹·n⁻¹·R⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·Θ·n·R
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "gravity": "1", "temperature": "-1", "amount": "-1", "gas_constant": "-1"}
6
concentration,gas_constant,gravity,length,mass,temperature
m·ℓ·g·Θ·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻²·g·Θ⁻¹·c_n⁻¹·R⁻¹
m = k₀ · ℓ²·g⁻¹·Θ·c_n·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "gravity": "1", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,gas_constant,gravity,length,mass,temperature
m·ℓ·g·Θ·R·z
chemistry,mechanics,thermo
m²·ℓ·g³·Θ⁻²·R⁻²·z⁻²
ℓ = k₀ · m⁻²·g⁻³·Θ²·R²·z²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "1", "gravity": "3", "temperature": "-2", "gas_constant": "-2", "cat_activity": "-2"}
6
avogadro,gas_constant,gravity,length,mass,temperature
m·ℓ·g·Θ·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ·g·Θ⁻¹·R⁻¹·N_A
m = k₀ · ℓ⁻¹·g⁻¹·Θ·R·N_A⁻¹
null
1
4
1
6
5.8
2.7
false
{"mass": "1", "length": "1", "gravity": "1", "temperature": "-1", "gas_constant": "-1", "avogadro": "1"}
5
boltzmann,gravity,length,mass,temperature
m·ℓ·g·Θ·k_B
constants,mechanics,thermo
m·ℓ·g·Θ⁻¹·k_B⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·Θ·k_B
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "gravity": "1", "temperature": "-1", "boltzmann": "-1"}
5
entropy,expansion,gravity,length,mass
m·ℓ·g·S_e·β
mechanics,thermo
m·ℓ·g·S_e⁻¹·β
m = k₀ · ℓ⁻¹·g⁻¹·S_e·β⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "gravity": "1", "entropy": "-1", "expansion": "1"}
6
entropy,gas_constant,gravity,length,mass,molar_energy
m·ℓ·g·S_e·E_m·R
chemistry,mechanics,thermo
m·ℓ·g·S_e⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻¹·g⁻¹·S_e·E_m·R⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "gravity": "1", "entropy": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
expansion,gravity,heat_capacity,length,mass
m·ℓ·g·C·β
mechanics,thermo
m·ℓ·g·C⁻¹·β
m = k₀ · ℓ⁻¹·g⁻¹·C·β⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "gravity": "1", "heat_capacity": "-1", "expansion": "1"}
6
gas_constant,gravity,heat_capacity,length,mass,molar_energy
m·ℓ·g·C·E_m·R
chemistry,mechanics,thermo
m·ℓ·g·C⁻¹·E_m⁻¹·R
m = k₀ · ℓ⁻¹·g⁻¹·C·E_m·R⁻¹
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "gravity": "1", "heat_capacity": "-1", "molar_energy": "-1", "gas_constant": "1"}
5
gravity,length,mass,specific_heat,thermal_cond
m·ℓ·g·c·κ
mechanics,thermo
m²·ℓ⁻³·g·c²·κ⁻²
g = k₀ · m⁻²·ℓ³·c⁻²·κ²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-3", "gravity": "1", "specific_heat": "2", "thermal_cond": "-2"}
6
cat_activity,gas_constant,gravity,length,mass,specific_heat
m·ℓ·g·c·R·z
chemistry,mechanics,thermo
m²·ℓ⁻¹·g·c²·R⁻²·z⁻²
ℓ = k₀ · m²·g·c²·R⁻²·z⁻²
null
0
3
2
10
8.5
0.5
false
{"mass": "2", "length": "-1", "gravity": "1", "specific_heat": "2", "gas_constant": "-2", "cat_activity": "-2"}
5
expansion,gravity,length,mass,thermal_cond
m·ℓ·g·κ·β
mechanics,thermo
m²·ℓ⁻¹·g³·κ⁻²·β²
ℓ = k₀ · m²·g³·κ⁻²·β²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-1", "gravity": "3", "thermal_cond": "-2", "expansion": "2"}
6
gas_constant,gravity,length,mass,molar_mass,thermal_cond
m·ℓ·g·κ·M_m·R
chemistry,mechanics,thermo
m²·ℓ⁻³·g·κ⁻²·M_m⁻²·R²
g = k₀ · m⁻²·ℓ³·κ²·M_m²·R⁻²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "-3", "gravity": "1", "thermal_cond": "-2", "molar_mass": "-2", "gas_constant": "2"}
6
gas_constant,gravity,length,mass,molar_energy,thermal_cond
m·ℓ·g·κ·E_m·R
chemistry,mechanics,thermo
m²·ℓ⁻¹·g³·κ⁻²·E_m⁻²·R²
ℓ = k₀ · m²·g³·κ⁻²·E_m⁻²·R²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "-1", "gravity": "3", "thermal_cond": "-2", "molar_energy": "-2", "gas_constant": "2"}
6
amount,expansion,gas_constant,gravity,length,mass
m·ℓ·g·β·n·R
chemistry,mechanics,thermo
m·ℓ·g·β·n⁻¹·R⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·β⁻¹·n·R
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "length": "1", "gravity": "1", "expansion": "1", "amount": "-1", "gas_constant": "-1"}
6
concentration,expansion,gas_constant,gravity,length,mass
m·ℓ·g·β·c_n·R
chemistry,mechanics,thermo
m·ℓ⁻²·g·β·c_n⁻¹·R⁻¹
m = k₀ · ℓ²·g⁻¹·β⁻¹·c_n·R
null
0
3
2
7
6.4
2.6
false
{"mass": "1", "length": "-2", "gravity": "1", "expansion": "1", "concentration": "-1", "gas_constant": "-1"}
6
cat_activity,expansion,gas_constant,gravity,length,mass
m·ℓ·g·β·R·z
chemistry,mechanics,thermo
m²·ℓ·g³·β²·R⁻²·z⁻²
ℓ = k₀ · m⁻²·g⁻³·β⁻²·R²·z²
null
0
3
3
12
10.4
-1.4
false
{"mass": "2", "length": "1", "gravity": "3", "expansion": "2", "gas_constant": "-2", "cat_activity": "-2"}
6
avogadro,expansion,gas_constant,gravity,length,mass
m·ℓ·g·β·R·N_A
chemistry,constants,mechanics,thermo
m·ℓ·g·β·R⁻¹·N_A
m = k₀ · ℓ⁻¹·g⁻¹·β⁻¹·R·N_A⁻¹
null
1
4
1
6
5.8
2.7
false
{"mass": "1", "length": "1", "gravity": "1", "expansion": "1", "gas_constant": "-1", "avogadro": "1"}
5
boltzmann,expansion,gravity,length,mass
m·ℓ·g·β·k_B
constants,mechanics,thermo
m·ℓ·g·β·k_B⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·β⁻¹·k_B
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "gravity": "1", "expansion": "1", "boltzmann": "-1"}
5
charge,gravity,length,mass,voltage
m·ℓ·g·q·U
em,mechanics
m·ℓ·g·q⁻¹·U⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·q·U
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "gravity": "1", "charge": "-1", "voltage": "-1"}
5
charge,gravity,length,mass,resistance
m·ℓ·g·q·R
em,mechanics
m²·ℓ³·g·q⁻⁴·R⁻²
g = k₀ · m⁻²·ℓ⁻³·q⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "3", "gravity": "1", "charge": "-4", "resistance": "-2"}
5
capacitance,charge,gravity,length,mass
m·ℓ·g·q·C_e
em,mechanics
m·ℓ·g·q⁻²·C_e
m = k₀ · ℓ⁻¹·g⁻¹·q²·C_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "gravity": "1", "charge": "-2", "capacitance": "1"}
5
bfield,charge,gravity,length,mass
m·ℓ·g·q·B
em,mechanics
m²·ℓ⁻¹·g·q⁻²·B⁻²
ℓ = k₀ · m²·g·q⁻²·B⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "length": "-1", "gravity": "1", "charge": "-2", "bfield": "-2"}
5
charge,gravity,length,mag_flux,mass
m·ℓ·g·q·Φ
em,mechanics
m²·ℓ³·g·q⁻²·Φ⁻²
g = k₀ · m⁻²·ℓ⁻³·q²·Φ²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "3", "gravity": "1", "charge": "-2", "mag_flux": "-2"}
5
charge,gravity,length,mass,permittivity
m·ℓ·g·q·ε
em,mechanics
m·ℓ²·g·q⁻²·ε
m = k₀ · ℓ⁻²·g⁻¹·q²·ε⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "2", "gravity": "1", "charge": "-2", "permittivity": "1"}
5
charge,conductivity,gravity,length,mass
m·ℓ·g·q·σ
em,mechanics
m²·ℓ⁵·g·q⁻⁴·σ²
g = k₀ · m⁻²·ℓ⁻⁵·q⁴·σ⁻²
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "5", "gravity": "1", "charge": "-4", "conductivity": "2"}
5
charge,gravity,length,mass,resistivity
m·ℓ·g·q·ρ_e
em,mechanics
m²·ℓ⁵·g·q⁻⁴·ρ_e⁻²
g = k₀ · m⁻²·ℓ⁻⁵·q⁴·ρ_e²
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "5", "gravity": "1", "charge": "-4", "resistivity": "-2"}
5
current,gravity,length,mass,voltage
m·ℓ·g·i·U
em,mechanics
m²·ℓ·g³·i⁻²·U⁻²
ℓ = k₀ · m⁻²·g⁻³·i²·U²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "1", "gravity": "3", "current": "-2", "voltage": "-2"}
5
current,gravity,length,mass,resistance
m·ℓ·g·i·R
em,mechanics
m²·ℓ·g³·i⁻⁴·R⁻²
ℓ = k₀ · m⁻²·g⁻³·i⁴·R²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "1", "gravity": "3", "current": "-4", "resistance": "-2"}
5
current,gravity,inductance,length,mass
m·ℓ·g·i·L_e
em,mechanics
m·ℓ·g·i⁻²·L_e⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·i²·L_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "gravity": "1", "current": "-2", "inductance": "-1"}
5
current,efield,gravity,length,mass
m·ℓ·g·i·E_f
em,mechanics
m²·ℓ⁻¹·g³·i⁻²·E_f⁻²
ℓ = k₀ · m²·g³·i⁻²·E_f⁻²
null
0
2
3
10
8.1
1.4
false
{"mass": "2", "length": "-1", "gravity": "3", "current": "-2", "efield": "-2"}
5
bfield,current,gravity,length,mass
m·ℓ·g·i·B
em,mechanics
m·ℓ⁻¹·g·i⁻¹·B⁻¹
m = k₀ · ℓ·g⁻¹·i·B
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "-1", "gravity": "1", "current": "-1", "bfield": "-1"}
5
current,gravity,length,mag_flux,mass
m·ℓ·g·i·Φ
em,mechanics
m·ℓ·g·i⁻¹·Φ⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·i·Φ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "length": "1", "gravity": "1", "current": "-1", "mag_flux": "-1"}
5
current,gravity,length,mass,permittivity
m·ℓ·g·i·ε
em,mechanics
m·ℓ·g²·i⁻²·ε
m = k₀ · ℓ⁻¹·g⁻²·i²·ε⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "gravity": "2", "current": "-2", "permittivity": "1"}
5
conductivity,current,gravity,length,mass
m·ℓ·g·i·σ
em,mechanics
m²·ℓ³·g³·i⁻⁴·σ²
m = k₀ · ℓ⁻³ᐟ²·g⁻³ᐟ²·i²·σ⁻¹
null
0
2
4
14
11.4
-1.9
false
{"mass": "2", "length": "3", "gravity": "3", "current": "-4", "conductivity": "2"}
5
current,gravity,length,mass,resistivity
m·ℓ·g·i·ρ_e
em,mechanics
m²·ℓ³·g³·i⁻⁴·ρ_e⁻²
m = k₀ · ℓ⁻³ᐟ²·g⁻³ᐟ²·i²·ρ_e
null
0
2
4
14
11.4
-1.9
false
{"mass": "2", "length": "3", "gravity": "3", "current": "-4", "resistivity": "-2"}
5
gravity,length,mass,resistance,voltage
m·ℓ·g·U·R
em,mechanics
m²·ℓ·g³·U⁻⁴·R²
ℓ = k₀ · m⁻²·g⁻³·U⁴·R⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "1", "gravity": "3", "voltage": "-4", "resistance": "2"}
5
capacitance,gravity,length,mass,voltage
m·ℓ·g·U·C_e
em,mechanics
m·ℓ·g·U⁻²·C_e⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·U²·C_e
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "gravity": "1", "voltage": "-2", "capacitance": "-1"}
5
gravity,length,mass,permeability,voltage
m·ℓ·g·U·μ₀
em,mechanics
m·ℓ·g²·U⁻²·μ₀
m = k₀ · ℓ⁻¹·g⁻²·U²·μ₀⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "1", "gravity": "2", "voltage": "-2", "permeability": "1"}
5
conductivity,gravity,length,mass,voltage
m·ℓ·g·U·σ
em,mechanics
m²·ℓ⁻¹·g³·U⁻⁴·σ⁻²
ℓ = k₀ · m²·g³·U⁻⁴·σ⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "-1", "gravity": "3", "voltage": "-4", "conductivity": "-2"}
5
gravity,length,mass,resistivity,voltage
m·ℓ·g·U·ρ_e
em,mechanics
m²·ℓ⁻¹·g³·U⁻⁴·ρ_e²
ℓ = k₀ · m²·g³·U⁻⁴·ρ_e²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "-1", "gravity": "3", "voltage": "-4", "resistivity": "2"}
5
elem_charge,gravity,length,mass,voltage
m·ℓ·g·U·e
constants,em,mechanics
m·ℓ·g·U⁻¹·e⁻¹
m = k₀ · ℓ⁻¹·g⁻¹·U·e
null
1
3
1
5
4.2
4.8
false
{"mass": "1", "length": "1", "gravity": "1", "voltage": "-1", "elem_charge": "-1"}
5
efield,gravity,length,mass,resistance
m·ℓ·g·R·E_f
em,mechanics
m²·ℓ⁻³·g³·R²·E_f⁻⁴
m = k₀ · ℓ³ᐟ²·g⁻³ᐟ²·R⁻¹·E_f²
null
0
2
4
14
11.4
-1.9
false
{"mass": "2", "length": "-3", "gravity": "3", "resistance": "2", "efield": "-4"}
5
bfield,gravity,length,mass,resistance
m·ℓ·g·R·B
em,mechanics
m²·ℓ⁻⁵·g·R²·B⁻⁴
g = k₀ · m⁻²·ℓ⁵·R⁻²·B⁴
null
0
2
5
14
11.9
-2.4
false
{"mass": "2", "length": "-5", "gravity": "1", "resistance": "2", "bfield": "-4"}
5
gravity,length,mag_flux,mass,resistance
m·ℓ·g·R·Φ
em,mechanics
m²·ℓ³·g·R²·Φ⁻⁴
g = k₀ · m⁻²·ℓ⁻³·R⁻²·Φ⁴
null
0
2
4
12
10
-0.5
false
{"mass": "2", "length": "3", "gravity": "1", "resistance": "2", "mag_flux": "-4"}
5
elem_charge,gravity,length,mass,resistance
m·ℓ·g·R·e
constants,em,mechanics
m²·ℓ³·g·R⁻²·e⁻⁴
g = k₀ · m⁻²·ℓ⁻³·R²·e⁴
null
1
3
4
12
10.6
-1.6
false
{"mass": "2", "length": "3", "gravity": "1", "resistance": "-2", "elem_charge": "-4"}
5
capacitance,efield,gravity,length,mass
m·ℓ·g·C_e·E_f
em,mechanics
m·ℓ⁻¹·g·C_e⁻¹·E_f⁻²
m = k₀ · ℓ·g⁻¹·C_e·E_f²
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "-1", "gravity": "1", "capacitance": "-1", "efield": "-2"}
5
capacitance,elem_charge,gravity,length,mass
m·ℓ·g·C_e·e
constants,em,mechanics
m·ℓ·g·C_e·e⁻²
m = k₀ · ℓ⁻¹·g⁻¹·C_e⁻¹·e²
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "length": "1", "gravity": "1", "capacitance": "1", "elem_charge": "-2"}
5
efield,gravity,inductance,length,mass
m·ℓ·g·L_e·E_f
em,mechanics
m·ℓ⁻²·g²·L_e·E_f⁻²
m = k₀ · ℓ²·g⁻²·L_e⁻¹·E_f²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "length": "-2", "gravity": "2", "inductance": "1", "efield": "-2"}
5
bfield,gravity,inductance,length,mass
m·ℓ·g·L_e·B
em,mechanics
m·ℓ⁻³·g·L_e·B⁻²
m = k₀ · ℓ³·g⁻¹·L_e⁻¹·B²
null
0
2
3
8
6.7
2.8
true
{"mass": "1", "length": "-3", "gravity": "1", "inductance": "1", "bfield": "-2"}
5
gravity,inductance,length,mag_flux,mass
m·ℓ·g·L_e·Φ
em,mechanics
m·ℓ·g·L_e·Φ⁻²
m = k₀ · ℓ⁻¹·g⁻¹·L_e⁻¹·Φ²
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "length": "1", "gravity": "1", "inductance": "1", "mag_flux": "-2"}
5
efield,gravity,length,mass,permittivity
m·ℓ·g·E_f·ε
em,mechanics
m·ℓ⁻²·g·E_f⁻²·ε⁻¹
m = k₀ · ℓ²·g⁻¹·E_f²·ε
null
0
2
2
7
5.5
4
true
{"mass": "1", "length": "-2", "gravity": "1", "efield": "-2", "permittivity": "-1"}