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

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

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

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

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

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

density === mass volume^-1

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

density === 6 (diameter²)^(-3/2) mass pi^-1

density === 6 mass pi^-1 (4 radius²)^(-3/2)

density === 3/2 area^-1 diameter² (diameter²)^(-3/2) mass

density === 6 area^-1 mass radius² (4 radius²)^(-3/2)

mass === density volume

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

mass === 1/6 density (diameter²)^(3/2) pi

mass === 1/6 density pi (4 radius²)^(3/2)

mass === 2/3 area density diameter^-2 (diameter²)^(3/2)

mass === 1/6 area density radius^-2 (4 radius²)^(3/2)

diameter === 2 radius

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

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

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

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

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

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

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

volume === density^-1 mass

volume === 1/6 (diameter²)^(3/2) pi

volume === 1/6 pi (4 radius²)^(3/2)

volume === 2/3 area diameter^-2 (diameter²)^(3/2)

volume === 1/6 area radius^-2 (4 radius²)^(3/2)

area === 1/4 diameter² pi

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

area === pi radius²

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

pi === 4 area diameter^-2

solve[(4 area pi^-1)^(3/2) pi === 6 volume, pi]

pi === area radius^-2

solve[(4 area pi^-1)^(3/2) pi === 6 density^-1 mass, pi]

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)^(2/3))^(1/2)
       = 
3.242931562233897 cm



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



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



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)^(2/3))^(1/2)
         = 
6.485863124467794 cm



diameter = -1 ((6 density^-1 mass pi^-1)^(2/3))^(1/2)
         = 
-6.485863124467794 cm



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



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



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