Wall Mounted Faucet Layout

Calculate, validate, and visualize wall-mounted faucet installation geometry, especially faucet reach L and outlet height H1 for product selection. Use when an agent needs to solve or check faucet reach, outlet height, basin depth, stream angle, wall setback, or drain position from K, W/WS, L, H1, H2, and theta, or generate an annotated SVG diagram for the result.

Source: https://github.com/starsy/wall-mounted-faucet-layout-skill

Diagram reference:

• English: assets/wall_mounted_faucet_geometry_v2.svg
• Chinese: assets/wall_mounted_faucet_geometry_v2_zh.svg

Purpose

Use this skill to calculate or validate the installation geometry of a wall-mounted faucet and basin.

Most faucet-selection questions should focus on:

• L: required faucet reach, when the basin/drain geometry and desired outlet height are known
• H1: required outlet height above the basin rim, when a candidate faucet reach is known

It can solve for:

• H1: vertical distance from the basin rim to the faucet outlet
• L: horizontal reach of the faucet outlet from the finished wall
• WS: horizontal distance from the rear inner basin wall to the drain center
• theta: water-flow angle measured from the vertical
• K: horizontal distance from the finished wall to the rear inner basin wall
• H2: vertical depth from the basin rim reference line to the target point at the drain

It can also use W, the front-to-back inner basin width, to assume a centered drain when WS is not supplied.

Coordinate convention

All linear measurements must use the same unit.

• Horizontal distance increases from the wall toward the front of the basin.
• Vertical distance increases downward from the faucet outlet toward the drain.
• theta is measured from the vertical direction.
• A positive theta means the water points forward, away from the wall.

Symbol	Meaning
K	Finished wall to rear inner basin wall
W	Front-to-back inner width of the basin
WS	Rear inner basin wall to drain center
L	Finished wall to faucet outlet
H1	Basin rim to faucet outlet, vertically upward
H2	Basin rim to drain target point, vertically downward
theta	Water angle from vertical, in degrees

If the drain is centered:

[ WS = \frac{W}{2} ]

Primary faucet-selection workflow

Prefer solving for L or H1 when the user is choosing a faucet:

• Solve for L when the user knows the desired outlet height or wall rough-in height. Use the result to compare against faucet reach/spec-sheet projection from the finished wall to the outlet.
• Solve for H1 when the user has a candidate faucet reach L. Use the result to decide whether the outlet height above the basin rim is practical.
• Do not treat H1 + H2 as a fixed recommended value. It is the vertical drop required by the selected horizontal geometry and stream angle.
• If the user asks generally for the "right faucet" and provides both a desired outlet height and basin/drain geometry, solve L first.
• If the user provides a faucet model or faucet reach, solve H1 first.

Core geometry

Horizontal offset:

[ \Delta x = K + WS - L ]

Vertical drop:

[ \Delta y = H1 + H2 ]

Core relationship:

[ \tan(\theta)=\frac{K+WS-L}{H1+H2} ]

This models the water path as a straight centerline. Real water flow curves under gravity and varies with pressure, aerator design, and flow rate.

Solving formulas

Solve for H1

[ H1=\frac{K+WS-L}{\tan(\theta)}-H2 ]

Solve for L

[ L=K+WS-(H1+H2)\tan(\theta) ]

Solve for WS

[ WS=L-K+(H1+H2)\tan(\theta) ]

Solve for theta

[ \theta=\arctan\left(\frac{K+WS-L}{H1+H2}\right) ]

Convert the result to degrees.

Solve for K

[ K=L-WS+(H1+H2)\tan(\theta) ]

Solve for H2

[ H2=\frac{K+WS-L}{\tan(\theta)}-H1 ]

Required calculation procedure

1. Identify the target variable. For faucet selection, prefer L or H1 unless the user explicitly asks for another variable.
2. Normalize all lengths to one unit.
3. Confirm that theta is measured from the vertical.
4. Resolve the drain location:
   • Use supplied WS; or
   • If WS is absent and W is supplied, set WS = W / 2.
5. Select the target formula.
6. Convert degrees to radians before calling a trigonometric function.
7. Calculate with a calculator or script.
8. Report the formula, substitution, exact result, and practical rounded result.
9. Run the validation checks.
10. Recommend an on-site water test before concealed installation.
11. When the user would benefit from a visual explanation or installation handoff, generate an annotated SVG with scripts/render_geometry_svg.py.

Validation checks

• Require all inputs needed by the selected formula.
• Require one consistent length unit.
• Normally require 0° < theta < 90° for forward flow.
• If W is known, require 0 < WS < W.
• If H1 < 0, the geometry or reference lines are incompatible.
• If K + WS - L < 0, the target point lies behind the outlet under this coordinate convention.

Reverse-check the result by substituting it into:

[ \tan(\theta)=\frac{K+WS-L}{H1+H2} ]

If W is known, report the drain offset from basin center:

[ \text{center offset}=WS-\frac{W}{2} ]

• Positive: forward of center
• Negative: rearward of center
• Zero: centered

Sensitivity

For fixed K, WS, H2, and theta:

[ \frac{\partial H1}{\partial L}=-\frac{1}{\tan(\theta)} ]

At theta = 10°:

[ \frac{1}{\tan(10^\circ)}\approx5.67 ]

So increasing L by 1 cm lowers theoretical H1 by about 5.67 cm.

Response template

Known:
K = ...
WS = ...  (or W = ... and WS = W/2)
H1 = ...
H2 = ...
L = ...
theta = ... degrees

Formula:
[target formula]

Substitution:
[...]

Result:
[target] = ... [unit]

Selection guidance:
- If solving L: compare this against faucet reach/spec-sheet projection from finished wall to outlet.
- If solving H1: compare this against the desired outlet height above the basin rim and available wall rough-in.

Validation:
- Horizontal offset Δx = ...
- Vertical drop Δy = ...
- Reverse check = ...
- Drain offset from basin center = ... (when W is known)

Practical note:
This is a straight-line geometric estimate. Confirm with a full-scale mock-up or water-flow test.

Visual SVG output

When the user asks for a visual, diagram, annotated layout, client handoff, or installer handoff, render a custom SVG with the included script. Use the same inputs and target variable that you used for the numeric calculation.

python scripts/render_geometry_svg.py --solve L --K 5 --WS 20 --H1 15 --H2 14 --theta 10 --unit cm --output faucet-layout.svg

The generated SVG marks the supplied dimensions, solved value, horizontal offset, vertical drop, reverse-check angle, and practical warning note directly in the diagram. Prefer writing the output to a user-visible path named for the project or scenario.

Worked examples

Example 1: choose faucet reach, solve for L

Given K=5 cm, WS=20 cm, H1=15 cm, H2=14 cm, theta=10°:

[ L=5+20-(15+14)\tan(10^\circ)\approx19.89\text{ cm} ]

Interpretation: choose a faucet whose outlet projects about 19.9 cm from the finished wall, then verify with real water flow.

Example 2: check mounting height, solve for H1

Given K=5 cm, W=40 cm, H2=14 cm, L=20.5 cm, theta=10°:

[ WS=20 ]

[ H1=\frac{5+20-20.5}{\tan(10^\circ)}-14\approx11.52\text{ cm} ]

Interpretation: this faucet reach works geometrically if the outlet can sit about 11.5 cm above the basin rim.

Example 3: short reach, solve for H1

Given K=5 cm, WS=20 cm, H2=14 cm, L=16 cm, theta=10°:

[ H1=\frac{5+20-16}{\tan(10^\circ)}-14\approx37.04\text{ cm} ]

The large result is expected because a 10-degree stream is close to vertical.

Example 4: secondary check, solve for WS

Given K=5 cm, H1=15 cm, H2=14 cm, L=20.5 cm, theta=10°:

[ WS=20.5-5+(15+14)\tan(10^\circ)\approx20.61\text{ cm} ]

For W=40 cm, the drain is approximately 0.61 cm forward of center.

Agent implementation note

Prefer deterministic calculation with the included script. Do not estimate trigonometric values mentally when exact dimensions matter.

The script calculates with full floating-point precision internally, then prints practical engineering precision by default:

• --unit mm: whole millimeters
• --unit cm: 0.1 cm
• --unit m: 0.001 m
• Angles: 0.1°

Use --precision or --angle-precision only when the user explicitly needs a different display precision.

Reference calculator:

scripts/faucet_geometry.py

Reference visual renderer:

scripts/render_geometry_svg.py

Primary calculator commands:

python scripts/faucet_geometry.py --solve L --K 5 --WS 20 --H1 15 --H2 14 --theta 10 --unit cm
python scripts/faucet_geometry.py --solve H1 --K 5 --W 40 --H2 14 --L 20.5 --theta 10 --unit cm