Convert pound / cubic meter to grain / cubic inch

Learn how to convert 1 pound / cubic meter to grain / cubic inch step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{p o u n d}{c u b i c m e t e r}) = x (\frac{g r a i n}{c u b i c i n c h})

Define the base values of the selected units in relation to the SI unit

(\frac{k i l o g r a m}{c u b i c m e t e r})

Left side: 1.0 (\frac{p o u n d}{c u b i c m e t e r}) = 0.5 (\frac{k i l o g r a m}{c u b i c m e t e r}) = 0.5 (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{c u b i c i n c h}) = \frac{6.479891}{1.6387064} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{1.6387064} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{p o u n d}{c u b i c m e t e r}) = x (\frac{g r a i n}{c u b i c i n c h})

Insert known values =>

1.0 \times 0.5 \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{6.479891}{1.6387064} \times (\frac{k i l o g r a m}{c u b i c m e t e r})

Or

1.0 \cdot 0.5 \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891}{1.6387064} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times 0.5 \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891}{1.6387064} \times (\frac{k g}{m^{3}})

Conversion Equation

0.5 = x \times \frac{6.479891}{1.6387064}

Switch sides

x \times \frac{6.479891}{1.6387064} = 0.5

Isolate

x

Multiply both sides by

(\frac{1.6387064}{6.479891})

x \times \frac{6.479891}{1.6387064} \times \frac{1.6387064}{6.479891} = 0.5 \times \frac{1.6387064}{6.479891}

Cancel

x \times \frac{6.479891 \times 1.6387064}{1.6387064 \times 6.479891} = 0.5 \times \frac{1.6387064}{6.479891}

Simplify

x = \frac{0.5 \times 1.6387064}{6.479891}

Solve

x

x \approx 0.126445522 \approx 1.2645 \times 10^{- 1}

Conversion Equation

1.0 (\frac{p o u n d}{c u b i c m e t e r}) \approx 1.2645 \times 10^{- 1} (\frac{g r a i n}{c u b i c i n c h})

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