Chapter 3, Problem 15P

To determine

Create a Table that shows wrench size in metric and U.S. units.

Explanation of Solution

Calculation:

Consider the general U.S. standard wrench sizes in ‘in.’:

The sizes are listed below which are normally used in U.S.

$1/4\text{'}\text{'},5/16\text{'}\text{'},7/16\text{'}\text{'},1/2\text{'}\text{'},9/16\text{'}\text{'},5/8\text{'}\text{'},3/4\text{'}\text{'},13/16\text{'}\text{'},15/16\text{'}\text{'},1\text{-}1/8\text{'}\text{'},1\text{-}5/16\text{'}\text{'},1\text{-}1/2\text{'}\text{'}$

$,1\text{-}11/16\text{'}\text{'},1\text{-}7/8\text{'}\text{'}$

The calculation for wrench size in metric and U.S. units are shown below:

For the wrench size $1/4\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}1/4\text{'}\text{'}=0.25\text{in}\text{.}\\ \text{=}0.25\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\left[\therefore 1\text{in}.=25.4\text{mm}\right]\\ =6.35\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}1/4\text{'}\text{'}=0.25\text{in}\text{.}\\ \text{=}0.25\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\left[\therefore 1\text{in}\text{=}\text{0}\text{.0833}\text{ft}\right]\\ =0.0208\text{ft}\end{array}$

For the wrench size $5/16\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}5/16\text{'}\text{'}=0.3125\text{in}\text{.}\\ \text{=}0.3125\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =7.937\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}5/16\text{'}\text{'}=0.25\text{in}\text{.}\\ \text{=}0.3125\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.026\text{ft}\end{array}$

For the wrench size $7/16\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}7/16\text{'}\text{'}=0.4375\text{in}\text{.}\\ \text{=}0.4375\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =11.11\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}7/16\text{'}\text{'}=0.4375\text{in}\text{.}\\ \text{=}0.4375\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.036\text{ft}\end{array}$

For the wrench size $1/2\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}1/2\text{'}\text{'}=0.5\text{in}\text{.}\\ \text{=}0.5\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =12.7\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}1/2\text{'}\text{'}=0.5\text{in}\text{.}\\ \text{=}0.5\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.042\text{ft}\end{array}$

For the wrench size $9/16\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}9/16\text{'}\text{'}=0.5625\text{in}\text{.}\\ \text{=}0.5625\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =14.28\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}9/16\text{'}\text{'}=0.5625\text{in}\text{.}\\ \text{=}0.5625\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.046\text{ft}\end{array}$

For the wrench size $5/8\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}5/8\text{'}\text{'}=0.625\text{in}\text{.}\\ \text{=}0.625\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =15.87\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}5/8\text{'}\text{'}=0.625\text{in}\text{.}\\ \text{=}0.625\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.052\text{ft}\end{array}$

For the wrench size $3/4\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}3/4\text{'}\text{'}=0.75\text{in}\text{.}\\ \text{=}0.75\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =19.05\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}3/4\text{'}\text{'}=0.75\text{in}\text{.}\\ \text{=}0.75\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.062\text{ft}\end{array}$

For the wrench size $13/16\text{'}\text{'}$:

Convert the wrench size from inch to mm

$\begin{array}{c}13/16\text{'}\text{'}=0.8125\text{in}\text{.}\\ \text{=}0.8125\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =20.63\text{mm}\end{array}$

Convert the wrench size from inch to foot

$\begin{array}{c}13/16\text{'}\text{'}=0.8125\text{in}\text{.}\\ \text{=}0.8125\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.067\text{ft}\end{array}$

For the wrench size $\frac{15}{{16}^{"}}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}15/16\text{'}\text{'}=0.9375\text{in}\text{.}\\ \text{=}0.9375\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =23.81\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}15/16\text{'}\text{'}=0.9375\text{in}\text{.}\\ \text{=}0.9375\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.078\text{ft}\end{array}$

For the wrench size $1\text{-}1/8\text{'}\text{'}$:

Convert the wrench size from inch to mm

$\begin{array}{c}1\text{-}1/8\text{'}\text{'}=\frac{9}{8^{"}}\\ \text{=}1.125\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =28.57\text{mm}\end{array}$

Convert the wrench size from inch to foot

$\begin{array}{c}1\text{-}1/8\text{'}\text{'}=\frac{9}{8^{"}}\\ \text{=}1.125\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.093\text{ft}\end{array}$

For the wrench size $1\text{-}5/16\text{'}\text{'}$:

Convert the wrench size from inch to mm

$\begin{array}{c}1\text{-}5/16\text{'}\text{'}=\frac{21}{{16}^{"}}\\ \text{=}1.3125\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =33.33\text{mm}\end{array}$

Convert the wrench size from inch to foot

$\begin{array}{c}1\text{-}5/16\text{'}\text{'}=\frac{21}{{16}^{"}}\\ \text{=}1.3125\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.109\text{ft}\end{array}$

For the wrench size $1\text{-}1/2\text{'}\text{'}$:

Convert the wrench size from inch to mm

$\begin{array}{c}1\text{-}1/2\text{'}\text{'}=\frac{3}{2^{"}}\\ \text{=}1.5\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =38.1\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}1\text{-}1/2\text{'}\text{'}=\frac{3}{2^{"}}\\ \text{=}1.5\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.124\text{ft}\end{array}$

For the wrench size $1\text{-}11/16\text{'}\text{'}$:

Convert the wrench size from inch to mm,

$\begin{array}{c}1\text{-}11/16\text{'}\text{'}=\frac{27}{{16}^{"}}\\ \text{=}1.6875\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =42.86\text{mm}\end{array}$

Convert the wrench size from inch to foot as,

$\begin{array}{c}1\text{-}11/16\text{'}\text{'}=\frac{27}{{16}^{"}}\\ \text{=}1.6875\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.14\text{ft}\end{array}$

For wrench size $1\text{-}7/8\text{'}\text{'}$:

Convert the wrench size from inch to mm

$\begin{array}{c}1\text{-}7/8\text{'}\text{'}=\frac{15}{8^{"}}\\ \text{=}1.875\text{in}.\times \frac{25.4\text{mm}}{1\text{in}\text{.}}\\ =47.62\text{mm}\end{array}$

Convert the wrench size from inch to foot

$\begin{array}{c}1\text{-}7/8\text{'}\text{'}=\frac{15}{8^{"}}\\ \text{=}1.875\text{in}\text{.}\times \frac{0.0833\text{ft}}{1\text{in}}\\ =0.156\text{ft}\end{array}$

Tthe calculated wrench sizes in metric and U.S. units are tabulated in Table 1.

Table 1

U.S. standard wrench sizes (in.)	Metric (mm)	U.S. units (ft)
1/4"	6.35	0.0208
5/16"	7.937	0.026
7/16"	11.11	0.036
1/2"	12.7	0.042
9/16"	14.28	0.046
5/8"	15.87	0.052
3/4"	19.05	0.062
13/16"	20.63	0.067
15/16"	23.81	0.078
1-1/8"	28.57	0.093
1-5/16"	33.33	0.109
1-1/2"	38.1	0.124
1-11/16"	42.86	0.14
1-7/8"	47.62	0.156

Conclusion:

Thus, the standard wrench sizes in metric and U.S. units are calculated and tabulated in Table 1.