Tree RPA Calculator: What It Does & How to Use It

The Tree RPA Calculator works out the Rainwater Pipe Area (RPA) needed for a building’s roof drainage system. You enter the roof’s effective catchment area, the local rainfall intensity, and a runoff coefficient, and it returns the minimum cross-sectional area of rainwater pipe required, usually in square centimeters or square inches. This is a simplified engineering tool that helps you size vertical downpipes for a given roof, not a full stormwater design package.

Formula

The calculator uses the rational method adapted for pipe sizing. The required pipe area (RPA) is:

RPA = (A × I × C) / 3600

• A = effective roof area (m²) – the plan area of the roof that drains to the pipe, adjusted for any slope factor.
• I = rainfall intensity (mm/h) – the design storm intensity for the location and return period.
• C = runoff coefficient – the fraction of rainfall that becomes runoff (typically 0.9–1.0 for roofs).
• RPA = required cross-sectional area of the pipe (cm²).

The division by 3600 converts the flow from m²·mm/h to cm²·m/s (since 1 m² × 1 mm/h = 0.001 m³/h, and 1 m³/h = 1/3600 m³/s, then using the continuity equation Q = V·A with a typical full-bore velocity of 1 m/s). This assumes the pipe flows full and at a velocity of 1 m/s, which is a common design simplification.

Worked Example

Using the default values from the calculator:

• A = 100 m²
• I = 75 mm/h
• C = 0.95

Step 1: Multiply the roof area by the rainfall intensity and runoff coefficient:
100 × 75 × 0.95 = 7125

Step 2: Divide by 3600 to get the pipe area in cm²:
7125 / 3600 = 1.979 cm²

So the required pipe area is approximately 1.98 cm².

Step 3 (optional): If you want a circular pipe, the diameter is:
2 × sqrt(1.979 / π) ≈ 2 × sqrt(0.630) ≈ 2 × 0.794 ≈ 1.59 cm

That means a circular downpipe with an internal diameter of about 1.6 cm (16 mm) would theoretically suffice – but in practice, you would choose a much larger standard pipe size to avoid clogging and to handle partial flow.

What the Result Tells You

The RPA value is the minimum cross-sectional area of the vertical pipe needed to carry the design flow if the pipe flows full at 1 m/s. In reality, vertical pipes rarely flow full, and building codes require a safety margin, so the actual pipe you install will be larger than the calculated RPA. For example, a standard 75 mm (3 in) PVC downpipe has an internal area of about 44 cm², which is far more than the 1.98 cm² from the example – that’s typical because the formula gives a theoretical minimum, not a recommended commercial size.

You can use the RPA to compare different pipe shapes: a rectangular gutter downspout with the same area will carry the same flow in theory, but shape affects hydraulic efficiency, especially under partial flow conditions.

When to Use This Calculator

Use this tool for preliminary sizing of vertical rainwater pipes (downspouts) for small buildings, sheds, or extensions. It is most useful when you are:

• Checking whether an existing downpipe is adequate for a new roof area.
• Planning a rainwater harvesting system and need to know the pipe size.
• Learning about roof drainage design and want a quick estimate.

It is not a substitute for a full drainage design. Real-world systems involve gutters, horizontal pipes, fittings, and slope, all of which affect capacity. Local building codes often specify minimum pipe sizes regardless of the calculated RPA – for example, many jurisdictions require a minimum 50 mm (2 in) diameter downpipe for any habitable building.

Common Mistakes and Misconceptions

One frequent error is using the roof’s sloped surface area instead of the plan (horizontal) area. Rain falls vertically, so the catchment area is the horizontal projection of the roof, not the actual surface area. For a 30° roof pitch, the plan area is about 87% of the surface area.

Another mistake is ignoring the runoff coefficient. While a roof is impervious, some water is lost to evaporation, ponding, and splashing – a coefficient of 0.95 is a good default, but if the roof has gravel or vegetation, use a lower value (0.5–0.8).

Also, the formula assumes the pipe flows full at 1 m/s. In practice, flow in a vertical downpipe is often annular (water clings to the walls), so the actual capacity is lower. Many designers use a safety factor of 2–3, meaning they double or triple the calculated RPA.

Limitations of the Formula

The RPA formula is a simplified version of the rational method. It does not account for:

• Gutter capacity and slope – gutters must be sized separately.
• Friction losses in the pipe – short vertical pipes have low friction, but long runs or bends add resistance.
• Rainfall intensity variation – the design storm intensity depends on location and return period (e.g., a 10-year storm vs. a 100-year storm).
• Wind-driven rain – can increase the effective catchment area on sloped roofs.

For a more accurate design, consult local plumbing codes or use a full hydraulic model. The calculator is a teaching tool and a quick check, not a final engineering decision.

How to Choose a Real Pipe Size

Once you have the RPA, you need to convert it to a commercially available pipe. Here’s a practical approach:

1. Calculate the RPA using the calculator.
2. Multiply by a safety factor of 2 to 3 (or follow your local code).
3. Look up standard pipe internal areas: a 50 mm (2 in) pipe has about 19.6 cm², 75 mm (3 in) has about 44.2 cm², 100 mm (4 in) has about 78.5 cm².
4. Choose the smallest standard pipe that is at least as large as the adjusted RPA.

For example, with an RPA of 1.98 cm², a safety factor of 3 gives 5.94 cm², so a 50 mm pipe would be more than sufficient. In practice, most residential downpipes are at least 50 mm or 65 mm, even for small roofs, to avoid clogging from leaves and debris.

Frequently Asked Questions

What does RPA stand for?

RPA stands for Rainwater Pipe Area – the cross-sectional area of a vertical rainwater pipe needed to carry a given flow. It is a standard term in plumbing and drainage engineering.

Is the runoff coefficient always 0.95?

No. 0.95 is typical for a smooth, impervious roof (e.g., metal or asphalt shingle). For gravel roofs, use 0.6–0.8; for green roofs, 0.3–0.5. The coefficient represents the fraction of rainfall that becomes runoff.

Can I use this for gutters?

No – this calculator sizes vertical downpipes only. Gutters are horizontal and have different flow characteristics. You need a gutter sizing calculator that considers slope and cross-section.

What if my roof is not rectangular?

Use the plan area – the horizontal projection of the roof. For a simple gable roof, multiply the length by the width of the building footprint. For complex shapes, divide into rectangles and sum the areas.

Why does the calculator give such a small pipe size?

Because it assumes the pipe flows full at 1 m/s, which rarely happens in practice. The result is a theoretical minimum. Always apply a safety factor and follow local codes, which often mandate a minimum pipe size (e.g., 50 mm) regardless of the calculation.

What rainfall intensity should I use?

Use the design storm intensity for your area, typically the 10-year or 100-year return period. You can get this from local meteorological data or building codes. In the absence of data, 75 mm/h is a common default for many regions, but always check local requirements.

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in a | Effective roof area | m² | 100 | 0
in r | Rainfall intensity | mm/h | 75 | 0
in c | Runoff coefficient | - | 0.95 | 0
out rpa | Required pipe area | cm² | (a * r * c) / 3600 | 2
out dia | Equivalent circular diameter | cm | 2 * sqrt(rpa / pi) | 2