**TI-84 Plus: Staircases**

Given the rise
(height from lower floor to upper floor), run (length of the staircase), and
desired riser height (how high each stair is), the program STAIRS calculates the
number risers needed, along with the width of each stair, the incline, and
finally illustrates the staircase. STAIRS is designed with inches and feet (US
units) in mind.

**Formulas**

Given: Rise, Run, Desired Rise Height (DRH)

Number of
Risers:

n = rise/DRH,
rounded to the nearest integer

Tread width:

TW = run/(n –
1)

Adjusted Riser
Height (ARH)

ARH = rise/n,
rounded to the nearest 1/16

^{th}
One way to
approach this:

ARH = round(16*frac(rise/n),0)*16
+ int(rise/n)

Incline:

θ = atan(RH/TW)

Other Calculations:

Stringer:

S = (n – 1)*√(ARH^2
+ TW^2)

Number of
Stairs:

N_stairs = n -
1

**TI-84 Plus Program: STAIRS**

Input: Rise, Run, Desired Riser Height. Keep the units consistent. (12 inches = 1 foot)

Output: Number of Risers (R), Tread width of each
stair (T), Adjusted Riser Height (H), Angle of Incline (θ)

* Adjusted
Riser Height is rounded to the nearest 1/16

^{th}(of an inch). This is accomplished by the line iPart(H)+round(16*fPart(H),0)/16.
The graph
screen shows the staircase. A stat plot
shows where each stair ends with X (L

**1**) representing the position and Y representing the height (L**2**).
The program
sets the TI-84 Plus to Degrees mode.

"EWS
2016-12-03"

Degree

Input
"RISE:",B

Input
"RUN:",A

Input "DESIRED
RISER HEIGHT:",H

round(B/H,0)→N

A/(N-1)→T

B/N→H

"ROUND H TO
1/16"

iPart(H)+round(16*fPart(H),0)/16→H

tan^-1(H/T)→θ

√(H²+T²)*(N-1)→S

Disp "NUMBER OF
RISERS:",N

Disp "TREAD
WIDTH:",T

Pause

Disp "ADJ.
RISER HEIGHT:",H

Disp
"ANGLE:",θ

Pause

{0}→L1:{0}→L2

.5→Xmin:A+.5→Xmax

.5→Ymin:B+.5→Ymax

ClrDraw

For(I,1,N-1)

augment(L1,{I*T})→L1

augment(L2,{I*H})→L2

End

PlotsOff

PlotsOn 1

Plot1(xyLine,L1,L2)

Line(0,0,A,0)

Line(A,0,A,B)

For(I,0,N-1)

Line(T*I,H*I,T*I,H*(I+1))

Line(T*I,H*(I+1),T*(I+1),H*(I+1))

End

DispGraph

**Examples**

All amounts are
in inches.

Example 1: Rise = 35 in, Run = 84 in, Desired Riser
Height = 7 in

Results: Number of Risers: 5, Tread width: 21 in,
Adjusted Riser Height: 7 in, θ ≈ 18.43495°

Example 1 is
shown in the screen shots above.

Example 2: Rise = 40 in, Run = 90 in, Desired Riser
Height = 7 in

Results: Number of Risers: 6, Tread width: 18 in,
Adjusted Riser Height: 6.6875 in,

θ ≈ 20.38143°

Example 3: Rise = 56 in, Run = 50 in, Desired Riser
Height = 6.5 in

Results: Number of Risers: 9, Tread width: 6.25 in,
Adjusted Riser Height: 6.25 in,

θ ≈ 45°

This program
was inspired by the Calculated Industries Construction Master 5 calculator

Eddie

This blog is
property of Edward Shore, 2016

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