Frink System Solver

Equations (one per line):
area = pi radius^2 volume = 4/3 pi radius^3 diameter = 2 radius mass = volume density
Solve for: (leave blank for all)
Show output as: Default Raw Frink notation MathML
Evaluate result numerically


radius === 1/2 diameter

radius === 1/2 (6 pi^-1 volume)^(1/3)

radius === ( -0.25000000000000005 - 0.4330127018922193 i ) (6 pi^-1 volume)^(1/3)

radius === ( -0.2499999999999999 + 0.43301270189221935 i ) (6 pi^-1 volume)^(1/3)

radius === 1/2 (4 area pi^-1)^(1/2)

radius === -1/2 (4 area pi^-1)^(1/2)

radius === 1/2 (6 density^-1 mass pi^-1)^(1/3)

radius === ( -0.25000000000000005 - 0.4330127018922193 i ) (6 density^-1 mass pi^-1)^(1/3)

radius === ( -0.2499999999999999 + 0.43301270189221935 i ) (6 density^-1 mass pi^-1)^(1/3)

density === mass volume^-1

density === 6 diameter^-3 mass pi^-1

density === 3/4 mass pi^-1 radius^-3

density === 6 mass (4 area pi^-1)^(-3/2) pi^-1

density === -6 mass (4 area pi^-1)^(-3/2) pi^-1

density === 3/2 area^-1 diameter^-1 mass

mass === density volume

mass === 1/6 density diameter³ pi

mass === 4/3 density pi radius³

mass === 1/6 density (4 area pi^-1)^(3/2) pi

mass === -1/6 density (4 area pi^-1)^(3/2) pi

mass === 2/3 area density diameter

diameter === 2 radius

diameter === (6 pi^-1 volume)^(1/3)

diameter === ( -0.5000000000000001 - 0.8660254037844386 i ) (6 pi^-1 volume)^(1/3)

diameter === ( -0.4999999999999998 + 0.8660254037844387 i ) (6 pi^-1 volume)^(1/3)

diameter === (4 area pi^-1)^(1/2)

diameter === -1 (4 area pi^-1)^(1/2)

diameter === (6 density^-1 mass pi^-1)^(1/3)

diameter === ( -0.5000000000000001 - 0.8660254037844386 i ) (6 density^-1 mass pi^-1)^(1/3)

diameter === ( -0.4999999999999998 + 0.8660254037844387 i ) (6 density^-1 mass pi^-1)^(1/3)

area === 1/4 diameter² pi

area === pi radius²

area === 1/4 pi (6 pi^-1 volume)^(2/3)

area === ( -0.12499999999999995475 + 0.2165063509461096933 i ) pi (6 pi^-1 volume)^(2/3)

area === ( -0.12500000000000007305 - 0.2165063509461095884 i ) pi (6 pi^-1 volume)^(2/3)

area === 1/4 (6 density^-1 mass pi^-1)^(2/3) pi

area === ( -0.12499999999999995475 + 0.2165063509461096933 i ) (6 density^-1 mass pi^-1)^(2/3) pi

area === ( -0.12500000000000007305 - 0.2165063509461095884 i ) (6 density^-1 mass pi^-1)^(2/3) pi

area === 3/2 diameter^-1 volume

area === 3/2 density^-1 diameter^-1 mass

volume === 1/6 diameter³ pi

volume === density^-1 mass

volume === 4/3 pi radius³

volume === 1/6 (4 area pi^-1)^(3/2) pi

volume === -1/6 (4 area pi^-1)^(3/2) pi

volume === 2/3 area diameter

pi === 6 diameter^-3 volume

pi === 4 area diameter^-2

pi === 3/4 radius^-3 volume

pi === 6 density^-1 diameter^-3 mass

pi === area radius^-2

Evaluated result:

Sym	Symbolic?	Value
area =	area
density =	density
diameter =	diameter
mass =	mass
pi =	pi
radius =	radius
volume =	volume

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radius = 1/2 (4 area pi^-1)^(1/2)
       = 
3.241022407214287 cm



radius = -1/2 (4 area pi^-1)^(1/2)
       = 
-3.241022407214287 cm



radius = 1/2 (6 density^-1 mass pi^-1)^(1/3)
       = 
3.242931562233897 cm



radius = ( -0.25000000000000005 - 0.4330127018922193 i ) (6 density^-1 mass pi^-1)^(1/3)
       = 
( -1.6214657811169488243 - 2.8084611156289109243 i ) cm



radius = ( -0.2499999999999999 + 0.43301270189221935 i ) (6 density^-1 mass pi^-1)^(1/3)
       = 
( -1.6214657811169478514 + 2.8084611156289112486 i ) cm



density = 6 mass (4 area pi^-1)^(-3/2) pi^-1
        = 
7012.377537620049669 m^-3 kg



density = -6 mass (4 area pi^-1)^(-3/2) pi^-1
        = 
-7012.377537620049669 m^-3 kg



mass = 1/6 density (4 area pi^-1)^(3/2) pi
     = 
0.99823490142200051056 kg



mass = -1/6 density (4 area pi^-1)^(3/2) pi
     = 
-0.99823490142200051056 kg



diameter = (4 area pi^-1)^(1/2)
         = 
6.482044814428574 cm



diameter = -1 (4 area pi^-1)^(1/2)
         = 
-6.482044814428574 cm



diameter = (6 density^-1 mass pi^-1)^(1/3)
         = 
6.485863124467794 cm



diameter = ( -0.5000000000000001 - 0.8660254037844386 i ) (6 density^-1 mass pi^-1)^(1/3)
         = 
( -3.2429315622338976486 - 5.6169222312578218485 i ) cm



diameter = ( -0.4999999999999998 + 0.8660254037844387 i ) (6 density^-1 mass pi^-1)^(1/3)
         = 
( -3.2429315622338957028 + 5.6169222312578224971 i ) cm



area = 1/4 (6 density^-1 mass pi^-1)^(2/3) pi
     = 
0.0033038889377317506824 m²



area = ( -0.12499999999999995475 + 0.2165063509461096933 i ) (6 density^-1 mass pi^-1)^(2/3) pi
     = 
( -0.0016519444688658747432 + 0.0028612517513580798757 i ) m²



area = ( -0.12500000000000007305 - 0.2165063509461095884 i ) (6 density^-1 mass pi^-1)^(2/3) pi
     = 
( -0.0016519444688658763066 - 0.0028612517513580784894 i ) m²



volume = density^-1 mass
       = 
1/7000 m³



volume = 1/6 (4 area pi^-1)^(3/2) pi
       = 
0.00014260498591742864436 m³



volume = -1/6 (4 area pi^-1)^(3/2) pi
       = 
-0.00014260498591742864436 m³