Stair worksheet

1. Number of risers: 14

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{110}{8}$$=13.75$$=\text{rounded up:}14$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{110}{14}$$=7.8571\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $14-1$$=13$

4. Spread the run you have evenly across the treads to get each tread's depth

   $\frac{155}{13}$$=11.9231\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{110}^2+{155}^2}$$=190.0658\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{7.8571}{11.9231}$$=33.38\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 7.8571+11.9231$$=27.64\text{\hspace{0.17em}in}$

2. Number of risers: 12

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{86}{7.6}$$=11.3158$$=\text{rounded up:}12$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{86}{12}$$=7.1667\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $12-1$$=11$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $11\times 9$$=99\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{86}^2+{99}^2}$$=131.1373\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{7.1667}{9}$$=38.53\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 7.1667+9$$=23.33\text{\hspace{0.17em}in}$

3. Number of risers: 14

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{100}{7.5}$$=13.3333$$=\text{rounded up:}14$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{100}{14}$$=7.1429\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $14-1$$=13$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $13\times 12$$=156\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{100}^2+{156}^2}$$=185.2998\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{7.1429}{12}$$=30.76\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 7.1429+12$$=26.29\text{\hspace{0.17em}in}$

4. Number of risers: 13

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{80}{6.4}$$=12.5$$=\text{rounded up:}13$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{80}{13}$$=6.1538\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $13-1$$=12$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $12\times 11$$=132\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{80}^2+{132}^2}$$=154.3503\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{6.1538}{11}$$=29.22\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 6.1538+11$$=23.31\text{\hspace{0.17em}in}$

5. Number of risers: 10

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{100}{11}$$=9.0909$$=\text{rounded up:}10$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{100}{10}$$=10\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $10-1$$=9$

4. Spread the run you have evenly across the treads to get each tread's depth

   $\frac{110}{9}$$=12.2222\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{100}^2+{110}^2}$$=148.6607\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{10}{12.2222}$$=39.29\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 10+12.2222$$=32.22\text{\hspace{0.17em}in}$

6. Number of risers: 16

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{140}{8.75}$$=16$$=\text{rounded up:}16$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{140}{16}$$=8.75\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $16-1$$=15$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $15\times 10$$=150\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{140}^2+{150}^2}$$=205.1828\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{8.75}{10}$$=41.19\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 8.75+10$$=27.5\text{\hspace{0.17em}in}$

7. Number of risers: 13

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{110}{8.5}$$=12.9412$$=\text{rounded up:}13$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{110}{13}$$=8.4615\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $13-1$$=12$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $12\times 10$$=120\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{110}^2+{120}^2}$$=162.7882\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{8.4615}{10}$$=40.24\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 8.4615+10$$=26.92\text{\hspace{0.17em}in}$

8. Number of risers: 22

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{110}{5}$$=22$$=\text{rounded up:}22$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{110}{22}$$=5\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $22-1$$=21$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $21\times 9$$=189\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{110}^2+{189}^2}$$=218.6801\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{5}{9}$$=29.05\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 5+9$$=19\text{\hspace{0.17em}in}$

9. Number of risers: 20

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{130}{6.6}$$=19.697$$=\text{rounded up:}20$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{130}{20}$$=6.5\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $20-1$$=19$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $19\times 12$$=228\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{130}^2+{228}^2}$$=262.4576\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{6.5}{12}$$=28.44\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 6.5+12$$=25\text{\hspace{0.17em}in}$

10. Number of risers: 26

1. Divide the total rise by your tallest allowed riser, and round up so no step is too tall

   $\frac{130}{5}$$=26$$=\text{rounded up:}26$

2. Divide the rise evenly across the risers, so every step is the same height

   $\frac{130}{26}$$=5\text{\hspace{0.17em}in}$

3. You need one fewer tread than risers, because the upper floor serves as the top step

   $26-1$$=25$

4. Multiply the number of treads by the tread depth to see how far the stair reaches

   $25\times 11$$=275\text{\hspace{0.17em}in}$

5. Find the stringer length, the side board along the steps, as the diagonal across the rise and run

   $\sqrt{{130}^2+{275}^2}$$=304.1792\text{\hspace{0.17em}in}$

6. Find how steep the stair is: the angle whose slope is riser height over tread depth

   $\text{arctan}\frac{5}{11}$$=24.44\text{\hspace{0.17em}°}$

7. Do a comfort check: 2 × riser + tread. This is a rule of thumb, not a code rule

   $2\times 5+11$$=21\text{\hspace{0.17em}in}$