Datasets:
RANDMEDIATION
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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
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19 values
n_const
int64
0
4
n_domains
int64
1
6
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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,capacitance,mass,power,voltage
m·a·P·U·C_e
em,mechanics
m·a²·P⁻²·U²·C_e
m = k₀ · a⁻²·P²·U⁻²·C_e⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "power": "-2", "voltage": "2", "capacitance": "1"}
5
acceleration,efield,mass,power,voltage
m·a·P·U·E_f
em,mechanics
m²·a³·P⁻²·U·E_f⁻¹
U = k₀ · m⁻²·a⁻³·P²·E_f
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-2", "voltage": "1", "efield": "-1"}
5
acceleration,bfield,mass,power,voltage
m·a·P·U·B
em,mechanics
m³·a⁴·P⁻³·U·B⁻¹
U = k₀ · m⁻³·a⁻⁴·P³·B
null
0
2
4
12
10
-0.5
false
{"mass": "3", "acceleration": "4", "power": "-3", "voltage": "1", "bfield": "-1"}
5
acceleration,mag_flux,mass,power,voltage
m·a·P·U·Φ
em,mechanics
m·a²·P⁻¹·U⁻¹·Φ
m = k₀ · a⁻²·P·U·Φ⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "power": "-1", "voltage": "-1", "mag_flux": "1"}
5
acceleration,mass,permeability,power,voltage
m·a·P·U·μ₀
em,mechanics
m·a·P⁻²·U²·μ₀⁻¹
m = k₀ · a⁻¹·P²·U⁻²·μ₀
null
0
2
2
7
5.5
4
true
{"mass": "1", "acceleration": "1", "power": "-2", "voltage": "2", "permeability": "-1"}
5
acceleration,conductivity,mass,power,voltage
m·a·P·U·σ
em,mechanics
m²·a³·P⁻¹·U⁻²·σ⁻¹
P = k₀ · m²·a³·U⁻²·σ⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-1", "voltage": "-2", "conductivity": "-1"}
5
acceleration,mass,power,resistivity,voltage
m·a·P·U·ρ_e
em,mechanics
m²·a³·P⁻¹·U⁻²·ρ_e
P = k₀ · m²·a³·U⁻²·ρ_e
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-1", "voltage": "-2", "resistivity": "1"}
5
acceleration,elem_charge,mass,power,voltage
m·a·P·U·e
constants,em,mechanics
m·a²·P⁻²·U·e
m = k₀ · a⁻²·P²·U⁻¹·e⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "acceleration": "2", "power": "-2", "voltage": "1", "elem_charge": "1"}
5
acceleration,capacitance,mass,power,resistance
m·a·P·R·C_e
em,mechanics
m·a²·P⁻¹·R·C_e
m = k₀ · a⁻²·P·R⁻¹·C_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "power": "-1", "resistance": "1", "capacitance": "1"}
5
acceleration,inductance,mass,power,resistance
m·a·P·R·L_e
em,mechanics
m·a²·P⁻¹·R⁻¹·L_e
m = k₀ · a⁻²·P·R·L_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "power": "-1", "resistance": "-1", "inductance": "1"}
5
acceleration,efield,mass,power,resistance
m·a·P·R·E_f
em,mechanics
m⁴·a⁶·P⁻³·R·E_f⁻²
R = k₀ · m⁻⁴·a⁻⁶·P³·E_f²
null
0
2
6
16
13.8
-4.3
false
{"mass": "4", "acceleration": "6", "power": "-3", "resistance": "1", "efield": "-2"}
5
acceleration,bfield,mass,power,resistance
m·a·P·R·B
em,mechanics
m⁶·a⁸·P⁻⁵·R·B⁻²
R = k₀ · m⁻⁶·a⁻⁸·P⁵·B²
null
0
2
8
22
19
-9.5
false
{"mass": "6", "acceleration": "8", "power": "-5", "resistance": "1", "bfield": "-2"}
5
acceleration,mag_flux,mass,power,resistance
m·a·P·R·Φ
em,mechanics
m²·a⁴·P⁻³·R⁻¹·Φ²
R = k₀ · m²·a⁴·P⁻³·Φ²
null
0
2
4
12
10
-0.5
false
{"mass": "2", "acceleration": "4", "power": "-3", "resistance": "-1", "mag_flux": "2"}
5
acceleration,mass,permittivity,power,resistance
m·a·P·R·ε
em,mechanics
m·a·P⁻¹·R⁻¹·ε⁻¹
m = k₀ · a⁻¹·P·R·ε
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "power": "-1", "resistance": "-1", "permittivity": "-1"}
5
acceleration,mass,permeability,power,resistance
m·a·P·R·μ₀
em,mechanics
m·a·P⁻¹·R·μ₀⁻¹
m = k₀ · a⁻¹·P·R⁻¹·μ₀
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "power": "-1", "resistance": "1", "permeability": "-1"}
5
acceleration,conductivity,mass,power,resistance
m·a·P·R·σ
em,mechanics
m²·a³·P⁻²·R⁻¹·σ⁻¹
R = k₀ · m²·a³·P⁻²·σ⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-2", "resistance": "-1", "conductivity": "-1"}
5
acceleration,mass,power,resistance,resistivity
m·a·P·R·ρ_e
em,mechanics
m²·a³·P⁻²·R⁻¹·ρ_e
R = k₀ · m²·a³·P⁻²·ρ_e
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-2", "resistance": "-1", "resistivity": "1"}
5
acceleration,elem_charge,mass,power,resistance
m·a·P·R·e
constants,em,mechanics
m²·a⁴·P⁻³·R·e²
R = k₀ · m⁻²·a⁻⁴·P³·e⁻²
null
1
3
4
12
10.6
-1.6
false
{"mass": "2", "acceleration": "4", "power": "-3", "resistance": "1", "elem_charge": "2"}
5
acceleration,capacitance,inductance,mass,power
m·a·P·C_e·L_e
em,mechanics
m²·a⁴·P⁻²·C_e·L_e
C_e = k₀ · m⁻²·a⁻⁴·P²·L_e⁻¹
null
0
2
4
10
8.6
0.9
false
{"mass": "2", "acceleration": "4", "power": "-2", "capacitance": "1", "inductance": "1"}
5
acceleration,capacitance,efield,mass,power
m·a·P·C_e·E_f
em,mechanics
m³·a⁴·P⁻²·C_e⁻¹·E_f⁻²
C_e = k₀ · m³·a⁴·P⁻²·E_f⁻²
null
0
2
4
12
10
-0.5
false
{"mass": "3", "acceleration": "4", "power": "-2", "capacitance": "-1", "efield": "-2"}
5
acceleration,bfield,capacitance,mass,power
m·a·P·C_e·B
em,mechanics
m⁵·a⁶·P⁻⁴·C_e⁻¹·B⁻²
C_e = k₀ · m⁵·a⁶·P⁻⁴·B⁻²
null
0
2
6
18
15.2
-5.7
false
{"mass": "5", "acceleration": "6", "power": "-4", "capacitance": "-1", "bfield": "-2"}
5
acceleration,capacitance,mag_flux,mass,power
m·a·P·C_e·Φ
em,mechanics
m³·a⁶·P⁻⁴·C_e·Φ²
C_e = k₀ · m⁻³·a⁻⁶·P⁴·Φ⁻²
null
0
2
6
16
13.8
-4.3
false
{"mass": "3", "acceleration": "6", "power": "-4", "capacitance": "1", "mag_flux": "2"}
5
acceleration,capacitance,mass,permittivity,power
m·a·P·C_e·ε
em,mechanics
m²·a³·P⁻²·C_e·ε⁻¹
C_e = k₀ · m⁻²·a⁻³·P²·ε
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-2", "capacitance": "1", "permittivity": "-1"}
5
acceleration,capacitance,conductivity,mass,power
m·a·P·C_e·σ
em,mechanics
m³·a⁵·P⁻³·C_e·σ⁻¹
C_e = k₀ · m⁻³·a⁻⁵·P³·σ
null
0
2
5
13
11.2
-1.7
false
{"mass": "3", "acceleration": "5", "power": "-3", "capacitance": "1", "conductivity": "-1"}
5
acceleration,capacitance,mass,power,resistivity
m·a·P·C_e·ρ_e
em,mechanics
m³·a⁵·P⁻³·C_e·ρ_e
C_e = k₀ · m⁻³·a⁻⁵·P³·ρ_e⁻¹
null
0
2
5
13
11.2
-1.7
false
{"mass": "3", "acceleration": "5", "power": "-3", "capacitance": "1", "resistivity": "1"}
5
acceleration,capacitance,elem_charge,mass,power
m·a·P·C_e·e
constants,em,mechanics
m·a²·P⁻²·C_e⁻¹·e²
m = k₀ · a⁻²·P²·C_e·e⁻²
null
1
3
2
8
6.8
2.2
false
{"mass": "1", "acceleration": "2", "power": "-2", "capacitance": "-1", "elem_charge": "2"}
5
acceleration,efield,inductance,mass,power
m·a·P·L_e·E_f
em,mechanics
m⁵·a⁸·P⁻⁴·L_e·E_f⁻²
L_e = k₀ · m⁻⁵·a⁻⁸·P⁴·E_f²
null
0
2
8
20
17.6
-8.1
false
{"mass": "5", "acceleration": "8", "power": "-4", "inductance": "1", "efield": "-2"}
5
acceleration,bfield,inductance,mass,power
m·a·P·L_e·B
em,mechanics
m⁷·a¹⁰·P⁻⁶·L_e·B⁻²
L_e = k₀ · m⁻⁷·a⁻¹⁰·P⁶·B²
null
0
2
10
26
22.8
-13.3
false
{"mass": "7", "acceleration": "10", "power": "-6", "inductance": "1", "bfield": "-2"}
5
acceleration,inductance,mag_flux,mass,power
m·a·P·L_e·Φ
em,mechanics
m·a²·P⁻²·L_e⁻¹·Φ²
m = k₀ · a⁻²·P²·L_e·Φ⁻²
null
0
2
2
8
6.2
3.3
true
{"mass": "1", "acceleration": "2", "power": "-2", "inductance": "-1", "mag_flux": "2"}
5
acceleration,inductance,mass,permeability,power
m·a·P·L_e·μ₀
em,mechanics
m²·a³·P⁻²·L_e·μ₀⁻¹
L_e = k₀ · m⁻²·a⁻³·P²·μ₀
null
0
2
3
9
7.4
2.1
false
{"mass": "2", "acceleration": "3", "power": "-2", "inductance": "1", "permeability": "-1"}
5
acceleration,conductivity,inductance,mass,power
m·a·P·L_e·σ
em,mechanics
m·a·P⁻¹·L_e⁻¹·σ⁻¹
m = k₀ · a⁻¹·P·L_e·σ
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "power": "-1", "inductance": "-1", "conductivity": "-1"}
5
acceleration,inductance,mass,power,resistivity
m·a·P·L_e·ρ_e
em,mechanics
m·a·P⁻¹·L_e⁻¹·ρ_e
m = k₀ · a⁻¹·P·L_e·ρ_e⁻¹
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "power": "-1", "inductance": "-1", "resistivity": "1"}
5
acceleration,elem_charge,inductance,mass,power
m·a·P·L_e·e
constants,em,mechanics
m³·a⁶·P⁻⁴·L_e·e²
L_e = k₀ · m⁻³·a⁻⁶·P⁴·e⁻²
null
1
3
6
16
14.4
-5.4
false
{"mass": "3", "acceleration": "6", "power": "-4", "inductance": "1", "elem_charge": "2"}
5
acceleration,bfield,efield,mass,power
m·a·P·E_f·B
em,mechanics
m·a·P⁻¹·E_f·B⁻¹
m = k₀ · a⁻¹·P·E_f⁻¹·B
null
0
2
1
5
3.6
5.9
true
{"mass": "1", "acceleration": "1", "power": "-1", "efield": "1", "bfield": "-1"}
5
acceleration,efield,mag_flux,mass,power
m·a·P·E_f·Φ
em,mechanics
m³·a⁵·P⁻³·E_f⁻¹·Φ
E_f = k₀ · m³·a⁵·P⁻³·Φ
null
0
2
5
13
11.2
-1.7
false
{"mass": "3", "acceleration": "5", "power": "-3", "efield": "-1", "mag_flux": "1"}
5
acceleration,efield,mass,permittivity,power
m·a·P·E_f·ε
em,mechanics
m⁵·a⁷·P⁻⁴·E_f⁻²·ε⁻¹
ε = k₀ · m⁵·a⁷·P⁻⁴·E_f⁻²
null
0
2
7
19
16.4
-6.9
false
{"mass": "5", "acceleration": "7", "power": "-4", "efield": "-2", "permittivity": "-1"}
5
acceleration,efield,mass,permeability,power
m·a·P·E_f·μ₀
em,mechanics
m³·a⁵·P⁻²·E_f⁻²·μ₀
μ₀ = k₀ · m⁻³·a⁻⁵·P²·E_f²
null
0
2
5
13
11.2
-1.7
false
{"mass": "3", "acceleration": "5", "power": "-2", "efield": "-2", "permeability": "1"}
5
acceleration,conductivity,efield,mass,power
m·a·P·E_f·σ
em,mechanics
m⁶·a⁹·P⁻⁵·E_f⁻²·σ⁻¹
σ = k₀ · m⁶·a⁹·P⁻⁵·E_f⁻²
null
0
2
9
23
20.2
-10.7
false
{"mass": "6", "acceleration": "9", "power": "-5", "efield": "-2", "conductivity": "-1"}
5
acceleration,efield,mass,power,resistivity
m·a·P·E_f·ρ_e
em,mechanics
m⁶·a⁹·P⁻⁵·E_f⁻²·ρ_e
ρ_e = k₀ · m⁻⁶·a⁻⁹·P⁵·E_f²
null
0
2
9
23
20.2
-10.7
false
{"mass": "6", "acceleration": "9", "power": "-5", "efield": "-2", "resistivity": "1"}
5
acceleration,bfield,mag_flux,mass,power
m·a·P·B·Φ
em,mechanics
m⁴·a⁶·P⁻⁴·B⁻¹·Φ
B = k₀ · m⁴·a⁶·P⁻⁴·Φ
null
0
2
6
16
13.8
-4.3
false
{"mass": "4", "acceleration": "6", "power": "-4", "bfield": "-1", "mag_flux": "1"}
5
acceleration,bfield,mass,permittivity,power
m·a·P·B·ε
em,mechanics
m⁷·a⁹·P⁻⁶·B⁻²·ε⁻¹
ε = k₀ · m⁷·a⁹·P⁻⁶·B⁻²
null
0
2
9
25
21.6
-12.1
false
{"mass": "7", "acceleration": "9", "power": "-6", "bfield": "-2", "permittivity": "-1"}
5
acceleration,bfield,mass,permeability,power
m·a·P·B·μ₀
em,mechanics
m⁵·a⁷·P⁻⁴·B⁻²·μ₀
μ₀ = k₀ · m⁻⁵·a⁻⁷·P⁴·B²
null
0
2
7
19
16.4
-6.9
false
{"mass": "5", "acceleration": "7", "power": "-4", "bfield": "-2", "permeability": "1"}
5
acceleration,bfield,conductivity,mass,power
m·a·P·B·σ
em,mechanics
m⁸·a¹¹·P⁻⁷·B⁻²·σ⁻¹
σ = k₀ · m⁸·a¹¹·P⁻⁷·B⁻²
null
0
2
11
29
25.4
-15.9
false
{"mass": "8", "acceleration": "11", "power": "-7", "bfield": "-2", "conductivity": "-1"}
5
acceleration,bfield,mass,power,resistivity
m·a·P·B·ρ_e
em,mechanics
m⁸·a¹¹·P⁻⁷·B⁻²·ρ_e
ρ_e = k₀ · m⁻⁸·a⁻¹¹·P⁷·B²
null
0
2
11
29
25.4
-15.9
false
{"mass": "8", "acceleration": "11", "power": "-7", "bfield": "-2", "resistivity": "1"}
5
acceleration,bfield,elem_charge,mass,power
m·a·P·B·e
constants,em,mechanics
m²·a²·P⁻¹·B⁻¹·e⁻¹
P = k₀ · m²·a²·B⁻¹·e⁻¹
null
1
3
2
7
6.1
2.9
false
{"mass": "2", "acceleration": "2", "power": "-1", "bfield": "-1", "elem_charge": "-1"}
5
acceleration,mag_flux,mass,permittivity,power
m·a·P·Φ·ε
em,mechanics
m·a³·P⁻²·Φ²·ε
m = k₀ · a⁻³·P²·Φ⁻²·ε⁻¹
null
0
2
3
9
7.4
2.1
false
{"mass": "1", "acceleration": "3", "power": "-2", "mag_flux": "2", "permittivity": "1"}
5
acceleration,mag_flux,mass,permeability,power
m·a·P·Φ·μ₀
em,mechanics
m³·a⁵·P⁻⁴·Φ²·μ₀⁻¹
μ₀ = k₀ · m³·a⁵·P⁻⁴·Φ²
null
0
2
5
15
12.6
-3.1
false
{"mass": "3", "acceleration": "5", "power": "-4", "mag_flux": "2", "permeability": "-1"}
5
acceleration,elem_charge,mag_flux,mass,power
m·a·P·Φ·e
constants,em,mechanics
m²·a⁴·P⁻³·Φ·e
Φ = k₀ · m⁻²·a⁻⁴·P³·e⁻¹
null
1
3
4
11
9.9
-0.9
false
{"mass": "2", "acceleration": "4", "power": "-3", "mag_flux": "1", "elem_charge": "1"}
5
acceleration,mass,permeability,permittivity,power
m·a·P·ε·μ₀
em,mechanics
m²·a²·P⁻²·ε⁻¹·μ₀⁻¹
ε = k₀ · m²·a²·P⁻²·μ₀⁻¹
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "acceleration": "2", "power": "-2", "permittivity": "-1", "permeability": "-1"}
5
acceleration,conductivity,mass,permittivity,power
m·a·P·ε·σ
em,mechanics
m·a²·P⁻¹·ε·σ⁻¹
m = k₀ · a⁻²·P·ε⁻¹·σ
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "power": "-1", "permittivity": "1", "conductivity": "-1"}
5
acceleration,mass,permittivity,power,resistivity
m·a·P·ε·ρ_e
em,mechanics
m·a²·P⁻¹·ε·ρ_e
m = k₀ · a⁻²·P·ε⁻¹·ρ_e⁻¹
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "power": "-1", "permittivity": "1", "resistivity": "1"}
5
acceleration,elem_charge,mass,permittivity,power
m·a·P·ε·e
constants,em,mechanics
m³·a⁵·P⁻⁴·ε⁻¹·e²
ε = k₀ · m³·a⁵·P⁻⁴·e²
null
1
3
5
15
13.2
-4.2
false
{"mass": "3", "acceleration": "5", "power": "-4", "permittivity": "-1", "elem_charge": "2"}
5
acceleration,conductivity,mass,permeability,power
m·a·P·μ₀·σ
em,mechanics
m³·a⁴·P⁻³·μ₀⁻¹·σ⁻¹
μ₀ = k₀ · m³·a⁴·P⁻³·σ⁻¹
null
0
2
4
12
10
-0.5
false
{"mass": "3", "acceleration": "4", "power": "-3", "permeability": "-1", "conductivity": "-1"}
5
acceleration,mass,permeability,power,resistivity
m·a·P·μ₀·ρ_e
em,mechanics
m³·a⁴·P⁻³·μ₀⁻¹·ρ_e
μ₀ = k₀ · m³·a⁴·P⁻³·ρ_e
null
0
2
4
12
10
-0.5
false
{"mass": "3", "acceleration": "4", "power": "-3", "permeability": "-1", "resistivity": "1"}
5
acceleration,elem_charge,mass,permeability,power
m·a·P·μ₀·e
constants,em,mechanics
m·a³·P⁻²·μ₀·e²
m = k₀ · a⁻³·P²·μ₀⁻¹·e⁻²
null
1
3
3
9
8
1
false
{"mass": "1", "acceleration": "3", "power": "-2", "permeability": "1", "elem_charge": "2"}
5
acceleration,conductivity,elem_charge,mass,power
m·a·P·σ·e
constants,em,mechanics
m⁴·a⁷·P⁻⁵·σ⁻¹·e²
σ = k₀ · m⁴·a⁷·P⁻⁵·e²
null
1
3
7
19
17
-8
false
{"mass": "4", "acceleration": "7", "power": "-5", "conductivity": "-1", "elem_charge": "2"}
5
acceleration,elem_charge,mass,power,resistivity
m·a·P·ρ_e·e
constants,em,mechanics
m⁴·a⁷·P⁻⁵·ρ_e·e²
ρ_e = k₀ · m⁻⁴·a⁻⁷·P⁵·e⁻²
null
1
3
7
19
17
-8
false
{"mass": "4", "acceleration": "7", "power": "-5", "resistivity": "1", "elem_charge": "2"}
5
acceleration,amount,concentration,mass,power
m·a·P·n·c_n
chemistry,mechanics
m⁶·a⁹·P⁻⁶·n·c_n⁻¹
n = k₀ · m⁻⁶·a⁻⁹·P⁶·c_n
null
0
2
9
23
20.2
-10.7
false
{"mass": "6", "acceleration": "9", "power": "-6", "amount": "1", "concentration": "-1"}
5
acceleration,amount,mass,molar_energy,power
m·a·P·n·E_m
chemistry,mechanics
m·a²·P⁻²·n·E_m
m = k₀ · a⁻²·P²·n⁻¹·E_m⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "1", "acceleration": "2", "power": "-2", "amount": "1", "molar_energy": "1"}
5
acceleration,amount,cat_activity,mass,power
m·a·P·n·z
chemistry,mechanics
m·a²·P⁻¹·n·z⁻¹
m = k₀ · a⁻²·P·n⁻¹·z
null
0
2
2
6
4.8
4.7
true
{"mass": "1", "acceleration": "2", "power": "-1", "amount": "1", "cat_activity": "-1"}
5
acceleration,concentration,mass,molar_mass,power
m·a·P·M_m·c_n
chemistry,mechanics
m⁷·a⁹·P⁻⁶·M_m⁻¹·c_n⁻¹
M_m = k₀ · m⁷·a⁹·P⁻⁶·c_n⁻¹
null
0
2
9
24
20.9
-11.4
false
{"mass": "7", "acceleration": "9", "power": "-6", "molar_mass": "-1", "concentration": "-1"}
5
acceleration,mass,molar_energy,molar_mass,power
m·a·P·M_m·E_m
chemistry,mechanics
m²·a²·P⁻²·M_m⁻¹·E_m
M_m = k₀ · m²·a²·P⁻²·E_m
null
0
2
2
8
6.2
3.3
true
{"mass": "2", "acceleration": "2", "power": "-2", "molar_mass": "-1", "molar_energy": "1"}
5
acceleration,cat_activity,mass,molar_mass,power
m·a·P·M_m·z
chemistry,mechanics
m²·a²·P⁻¹·M_m⁻¹·z⁻¹
P = k₀ · m²·a²·M_m⁻¹·z⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "power": "-1", "molar_mass": "-1", "cat_activity": "-1"}
5
acceleration,concentration,mass,molar_energy,power
m·a·P·c_n·E_m
chemistry,mechanics
m⁵·a⁷·P⁻⁴·c_n⁻¹·E_m⁻¹
c_n = k₀ · m⁵·a⁷·P⁻⁴·E_m⁻¹
null
0
2
7
18
15.7
-6.2
false
{"mass": "5", "acceleration": "7", "power": "-4", "concentration": "-1", "molar_energy": "-1"}
6
acceleration,boltzmann,concentration,gas_constant,mass,power
m·a·P·c_n·R·k_B
chemistry,constants,mechanics
m⁶·a⁹·P⁻⁶·c_n⁻¹·R⁻¹·k_B
c_n = k₀ · m⁶·a⁹·P⁻⁶·R⁻¹·k_B
null
1
3
9
24
21.8
-12.8
false
{"mass": "6", "acceleration": "9", "power": "-6", "concentration": "-1", "gas_constant": "-1", "boltzmann": "1"}
5
acceleration,cat_activity,concentration,mass,power
m·a·P·c_n·z
chemistry,mechanics
m⁵·a⁷·P⁻⁵·c_n⁻¹·z
c_n = k₀ · m⁵·a⁷·P⁻⁵·z
null
0
2
7
19
16.4
-6.9
false
{"mass": "5", "acceleration": "7", "power": "-5", "concentration": "-1", "cat_activity": "1"}
5
acceleration,avogadro,concentration,mass,power
m·a·P·c_n·N_A
chemistry,constants,mechanics
m⁶·a⁹·P⁻⁶·c_n⁻¹·N_A⁻¹
c_n = k₀ · m⁶·a⁹·P⁻⁶·N_A⁻¹
null
1
3
9
23
20.8
-11.8
false
{"mass": "6", "acceleration": "9", "power": "-6", "concentration": "-1", "avogadro": "-1"}
6
acceleration,boltzmann,gas_constant,mass,molar_energy,power
m·a·P·E_m·R·k_B
chemistry,constants,mechanics
m·a²·P⁻²·E_m·R⁻¹·k_B
m = k₀ · a⁻²·P²·E_m⁻¹·R·k_B⁻¹
null
1
3
2
8
7.1
1.9
false
{"mass": "1", "acceleration": "2", "power": "-2", "molar_energy": "1", "gas_constant": "-1", "boltzmann": "1"}
5
acceleration,avogadro,mass,molar_energy,power
m·a·P·E_m·N_A
chemistry,constants,mechanics
m·a²·P⁻²·E_m·N_A⁻¹
m = k₀ · a⁻²·P²·E_m⁻¹·N_A
null
1
3
2
7
6.1
2.9
false
{"mass": "1", "acceleration": "2", "power": "-2", "molar_energy": "1", "avogadro": "-1"}
6
acceleration,boltzmann,cat_activity,gas_constant,mass,power
m·a·P·R·z·k_B
chemistry,constants,mechanics
m·a²·P⁻¹·R⁻¹·z⁻¹·k_B
m = k₀ · a⁻²·P·R·z·k_B⁻¹
null
1
3
2
7
6.4
2.6
false
{"mass": "1", "acceleration": "2", "power": "-1", "gas_constant": "-1", "cat_activity": "-1", "boltzmann": "1"}
5
acceleration,avogadro,cat_activity,mass,power
m·a·P·z·N_A
chemistry,constants,mechanics
m·a²·P⁻¹·z⁻¹·N_A⁻¹
m = k₀ · a⁻²·P·z·N_A
null
1
3
2
6
5.4
3.6
false
{"mass": "1", "acceleration": "2", "power": "-1", "cat_activity": "-1", "avogadro": "-1"}
5
acceleration,illuminance,lum_intensity,mass,power
m·a·P·I_v·E_v
mechanics,photometry
m⁴·a⁶·P⁻⁴·I_v·E_v⁻¹
I_v = k₀ · m⁻⁴·a⁻⁶·P⁴·E_v
null
0
2
6
16
13.8
-4.3
false
{"mass": "4", "acceleration": "6", "power": "-4", "lum_intensity": "1", "illuminance": "-1"}
5
acceleration,lum_intensity,luminance,mass,power
m·a·P·I_v·L_v
mechanics,photometry
m⁴·a⁶·P⁻⁴·I_v·L_v⁻¹
I_v = k₀ · m⁻⁴·a⁻⁶·P⁴·L_v
null
0
2
6
16
13.8
-4.3
false
{"mass": "4", "acceleration": "6", "power": "-4", "lum_intensity": "1", "luminance": "-1"}
4
acceleration,light_speed,mass,power
m·a·P·c₀
constants,mechanics
m·a·P⁻¹·c₀
m = k₀ · a⁻¹·P·c₀⁻¹
null
1
2
1
4
2.6
6.9
true
{"mass": "1", "acceleration": "1", "power": "-1", "light_speed": "1"}
4
acceleration,grav_const,mass,power
m·a·P·G
constants,mechanics
m⁵·a⁵·P⁻⁴·G
G = k₀ · m⁻⁵·a⁻⁵·P⁴
null
1
2
5
15
12.3
-2.8
false
{"mass": "5", "acceleration": "5", "power": "-4", "grav_const": "1"}
4
acceleration,mass,planck,power
m·a·P·h
constants,mechanics
m²·a⁴·P⁻³·h
h = k₀ · m⁻²·a⁻⁴·P³
null
1
2
4
10
8.3
1.2
false
{"mass": "2", "acceleration": "4", "power": "-3", "planck": "1"}
4
acceleration,ang_momentum,mass,momentum
m·a·p·Lₐ
mechanics
m²·a·p⁻³·Lₐ
a = k₀ · m⁻²·p³·Lₐ⁻¹
null
0
1
3
7
5.1
4.9
true
{"mass": "2", "acceleration": "1", "momentum": "-3", "ang_momentum": "1"}
4
acceleration,action,mass,momentum
m·a·p·S
mechanics
m²·a·p⁻³·S
a = k₀ · m⁻²·p³·S⁻¹
null
0
1
3
7
5.1
4.9
true
{"mass": "2", "acceleration": "1", "momentum": "-3", "action": "1"}
4
acceleration,inertia,mass,momentum
m·a·p·J
mechanics
m³·a²·p⁻⁴·J
J = k₀ · m⁻³·a⁻²·p⁴
null
0
1
4
10
7.7
2.3
false
{"mass": "3", "acceleration": "2", "momentum": "-4", "inertia": "1"}
4
acceleration,mass,momentum,pressure
m·a·p·P_p
mechanics
m⁵·a³·p⁻⁴·P_p⁻¹
P_p = k₀ · m⁵·a³·p⁻⁴
null
0
1
5
13
10.3
-0.3
false
{"mass": "5", "acceleration": "3", "momentum": "-4", "pressure": "-1"}
4
acceleration,density,mass,momentum
m·a·p·ρ
mechanics
m⁷·a³·p⁻⁶·ρ⁻¹
ρ = k₀ · m⁷·a³·p⁻⁶
null
0
1
7
17
14.1
-4.1
false
{"mass": "7", "acceleration": "3", "momentum": "-6", "density": "-1"}
4
acceleration,mass,momentum,viscosity
m·a·p·μ
mechanics
m⁴·a²·p⁻³·μ⁻¹
μ = k₀ · m⁴·a²·p⁻³
null
0
1
4
10
7.7
2.3
false
{"mass": "4", "acceleration": "2", "momentum": "-3", "viscosity": "-1"}
4
acceleration,kin_viscosity,mass,momentum
m·a·p·ν
mechanics
m³·a·p⁻³·ν
a = k₀ · m⁻³·p³·ν⁻¹
null
0
1
3
8
5.8
4.2
true
{"mass": "3", "acceleration": "1", "momentum": "-3", "kin_viscosity": "1"}
4
acceleration,mass,momentum,omega
m·a·p·ω
mechanics
m·a·p⁻¹·ω⁻¹
m = k₀ · a⁻¹·p·ω
null
0
1
1
4
2
8
true
{"mass": "1", "acceleration": "1", "momentum": "-1", "omega": "-1"}
4
acceleration,frequency,mass,momentum
m·a·p·f
mechanics
m·a·p⁻¹·f⁻¹
m = k₀ · a⁻¹·p·f
null
0
1
1
4
2
8
true
{"mass": "1", "acceleration": "1", "momentum": "-1", "frequency": "-1"}
4
acceleration,mass,momentum,stiffness
m·a·p·k
mechanics
m³·a²·p⁻²·k⁻¹
k = k₀ · m³·a²·p⁻²
null
0
1
3
8
5.8
4.2
true
{"mass": "3", "acceleration": "2", "momentum": "-2", "stiffness": "-1"}
4
acceleration,mass,momentum,surf_tension
m·a·p·γ
mechanics
m³·a²·p⁻²·γ⁻¹
γ = k₀ · m³·a²·p⁻²
null
0
1
3
8
5.8
4.2
true
{"mass": "3", "acceleration": "2", "momentum": "-2", "surf_tension": "-1"}
4
acceleration,area,mass,momentum
m·a·p·A
mechanics
m⁴·a²·p⁻⁴·A
A = k₀ · m⁻⁴·a⁻²·p⁴
null
0
1
4
11
8.4
1.6
false
{"mass": "4", "acceleration": "2", "momentum": "-4", "area": "1"}
4
acceleration,mass,momentum,volume
m·a·p·V
mechanics
m⁶·a³·p⁻⁶·V
V = k₀ · m⁻⁶·a⁻³·p⁶
null
0
1
6
16
12.9
-2.9
false
{"mass": "6", "acceleration": "3", "momentum": "-6", "volume": "1"}
4
acceleration,flowrate,mass,momentum
m·a·p·Q
mechanics
m⁵·a²·p⁻⁵·Q
Q = k₀ · m⁻⁵·a⁻²·p⁵
null
0
1
5
13
10.3
-0.3
false
{"mass": "5", "acceleration": "2", "momentum": "-5", "flowrate": "1"}
5
acceleration,mass,momentum,temperature,thermal_cond
m·a·p·Θ·κ
mechanics,thermo
m²·a²·p⁻¹·Θ⁻¹·κ⁻¹
p = k₀ · m²·a²·Θ⁻¹·κ⁻¹
null
0
2
2
7
5.5
4
true
{"mass": "2", "acceleration": "2", "momentum": "-1", "temperature": "-1", "thermal_cond": "-1"}
6
acceleration,concentration,gas_constant,mass,momentum,temperature
m·a·p·Θ·c_n·R
chemistry,mechanics,thermo
m⁵·a³·p⁻⁴·Θ⁻¹·c_n⁻¹·R⁻¹
Θ = k₀ · m⁵·a³·p⁻⁴·c_n⁻¹·R⁻¹
null
0
3
5
15
13.5
-4.5
false
{"mass": "5", "acceleration": "3", "momentum": "-4", "temperature": "-1", "concentration": "-1", "gas_constant": "-1"}
5
acceleration,entropy,mass,momentum,thermal_cond
m·a·p·S_e·κ
mechanics,thermo
m³·a²·p⁻³·S_e·κ⁻¹
S_e = k₀ · m⁻³·a⁻²·p³·κ
null
0
2
3
10
8.1
1.4
false
{"mass": "3", "acceleration": "2", "momentum": "-3", "entropy": "1", "thermal_cond": "-1"}
6
acceleration,concentration,entropy,gas_constant,mass,momentum
m·a·p·S_e·c_n·R
chemistry,mechanics,thermo
m⁶·a³·p⁻⁶·S_e·c_n⁻¹·R⁻¹
S_e = k₀ · m⁻⁶·a⁻³·p⁶·c_n·R
null
0
3
6
18
16.1
-7.1
false
{"mass": "6", "acceleration": "3", "momentum": "-6", "entropy": "1", "concentration": "-1", "gas_constant": "-1"}
6
acceleration,cat_activity,entropy,gas_constant,mass,momentum
m·a·p·S_e·R·z
chemistry,mechanics,thermo
m·a·p⁻¹·S_e·R⁻¹·z⁻¹
m = k₀ · a⁻¹·p·S_e⁻¹·R·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "acceleration": "1", "momentum": "-1", "entropy": "1", "gas_constant": "-1", "cat_activity": "-1"}
5
acceleration,heat_capacity,mass,momentum,thermal_cond
m·a·p·C·κ
mechanics,thermo
m³·a²·p⁻³·C·κ⁻¹
C = k₀ · m⁻³·a⁻²·p³·κ
null
0
2
3
10
8.1
1.4
false
{"mass": "3", "acceleration": "2", "momentum": "-3", "heat_capacity": "1", "thermal_cond": "-1"}
6
acceleration,concentration,gas_constant,heat_capacity,mass,momentum
m·a·p·C·c_n·R
chemistry,mechanics,thermo
m⁶·a³·p⁻⁶·C·c_n⁻¹·R⁻¹
C = k₀ · m⁻⁶·a⁻³·p⁶·c_n·R
null
0
3
6
18
16.1
-7.1
false
{"mass": "6", "acceleration": "3", "momentum": "-6", "heat_capacity": "1", "concentration": "-1", "gas_constant": "-1"}
6
acceleration,cat_activity,gas_constant,heat_capacity,mass,momentum
m·a·p·C·R·z
chemistry,mechanics,thermo
m·a·p⁻¹·C·R⁻¹·z⁻¹
m = k₀ · a⁻¹·p·C⁻¹·R·z
null
0
3
1
6
5.2
3.8
false
{"mass": "1", "acceleration": "1", "momentum": "-1", "heat_capacity": "1", "gas_constant": "-1", "cat_activity": "-1"}
5
acceleration,mass,momentum,specific_heat,thermal_cond
m·a·p·c·κ
mechanics,thermo
m⁴·a²·p⁻³·c·κ⁻¹
c = k₀ · m⁻⁴·a⁻²·p³·κ
null
0
2
4
11
9.3
0.2
false
{"mass": "4", "acceleration": "2", "momentum": "-3", "specific_heat": "1", "thermal_cond": "-1"}
6
acceleration,concentration,gas_constant,mass,momentum,specific_heat
m·a·p·c·c_n·R
chemistry,mechanics,thermo
m⁷·a³·p⁻⁶·c·c_n⁻¹·R⁻¹
c = k₀ · m⁻⁷·a⁻³·p⁶·c_n·R
null
0
3
7
19
17.3
-8.3
false
{"mass": "7", "acceleration": "3", "momentum": "-6", "specific_heat": "1", "concentration": "-1", "gas_constant": "-1"}