Use this firring calculator to work out the fall, the firring depth at each end, the roof gradient, the slope and the roof angle for a flat roof. Enter the roof run, pick a fall ratio such as 1:40, 1:60 or 1:80 (or type your own), and enter the low-end firring depth. The calculator returns the total fall and the high-end firring depth you need.
It can also work backwards from a known fall to the gradient, and its quantity mode estimates the number of firring lines and the total linear material, with an optional waste allowance. Imperial (feet and inches) and metric (metres and millimetres) are both supported. The formulas, a gradient reference table, worked examples and common mistakes are explained below.
Firring Calculator
Calculate flat roof fall, firring depth, roof gradient, and firring material quantity.
Firring Material Quantity
Calculation
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What Is Firring?
Firring is a tapered timber strip fixed to flat-roof joists to create a fall. One end is shallow and the other deeper, so the roof deck laid over it slopes towards the drainage point instead of sitting dead level.
Firring is not the same as furring. Furring strips are usually uniform battens used for spacing, levelling or giving a fixing surface, and a furring strip calculator solves a different quantity problem. Use a firring calculation when you need a taper that produces a specific fall.
How to Use the Firring Calculator
- Choose your units. Imperial takes the run and width in feet and the depths, fall and spacing in inches. Metric takes metres and millimetres. Switching converts the values already entered.
- Pick a calculation method: Calculate Firring Size, Calculate From Known Fall, or Calculate Firring Quantity.
- Enter the roof run. This is the horizontal distance in the direction of the fall, not the roof area.
- Select the fall gradient (1:40, 1:50, 1:60, 1:80, 1:100 or Custom), or enter the required total fall in Known Fall mode.
- Enter the low-end firring depth, the thickness at the shallow end.
- For quantity, also enter the roof width, firring spacing and a waste allowance, then select Calculate Firring.
Firring Calculator Modes
Calculate Firring Size
Enter the run, gradient and low-end depth. The calculator returns the total fall, the high-end depth, the fall per foot or metre, the slope percentage and the roof angle.
Calculate From Known Fall
Use this when the total fall is fixed, for example by the height available at an upstand. Enter the run, total fall and low-end depth, and the calculator works out the equivalent gradient using N = Run ÷ Total Fall, in the same units.
Calculate Firring Quantity
This adds the roof width, firring spacing and waste allowance to the size calculation. It returns the number of firring lines, the length per line, the base material and the material including waste.
How to Calculate Firring Depth
Step 1: Total Fall
Total Fall = Run ÷ N, for a 1:N gradient
The run and the fall must be in the same unit, so convert the run first: metres × 1,000 gives millimetres, and feet × 12 gives inches. For a 6 m run at 1:60: 6,000 ÷ 60 = 100 mm of fall.
Step 2: High-End Depth
High-End Depth = Low-End Depth + Total Fall
With a 25 mm low end: 25 + 100 = 125 mm. The firring tapers from 25 mm to 125 mm over the 6 m run. In imperial, a 10 ft run at 1:60 with a 1 in low end gives (10 × 12) ÷ 60 = 2 in of fall and a 3 in high end. These are the calculator’s default values.
What Do 1:40, 1:60 and 1:80 Mean?
A 1:N gradient falls 1 unit vertically for every N units of horizontal run. The smaller N is, the steeper the fall: over the same run, 1:40 gives twice the fall of 1:80. The table shows the preset gradients in the calculator.
| Gradient | Fall per metre | Fall per foot | Slope | Angle | Fall over 6 m |
|---|---|---|---|---|---|
| 1:40 | 25 mm | 0.3 in | 2.5% | 1.43° | 150 mm |
| 1:50 | 20 mm | 0.24 in | 2% | 1.15° | 120 mm |
| 1:60 | 16.67 mm | 0.2 in | 1.67% | 0.95° | 100 mm |
| 1:80 | 12.5 mm | 0.15 in | 1.25% | 0.72° | 75 mm |
| 1:100 | 10 mm | 0.12 in | 1% | 0.57° | 60 mm |
The calculator works out the geometry of the gradient you choose. It does not decide which gradient your roof needs. That comes from the roof design, the roofing or membrane system, the drainage layout and the requirements that apply to the project.
Worked Firring Examples
4 m Run at 1:40
4,000 ÷ 40 = 100 mm fall. With a 25 mm low end, the high end is 125 mm. Fall per metre is 25 mm and the slope is 2.5%.
4 m Run at 1:80
4,000 ÷ 80 = 50 mm fall. With a 25 mm low end, the high end is 75 mm, with 12.5 mm per metre and a 1.25% slope.
7 m Run at a Custom 1:70
Choose Custom and enter 70. 7,000 ÷ 70 = 100 mm fall, so a 25 mm low end rises to 125 mm. The fall per metre is 14.29 mm, the slope 1.43% and the angle 0.82°.
Fall per Unit, Slope and Roof Angle
These results describe the same slope in different ways.
Fall per Metre or Foot
Fall per metre = 1,000 ÷ N (mm/m) and fall per foot = 12 ÷ N (in/ft). At 1:60 that is 16.67 mm per metre, or 0.2 in per foot.
Slope Percentage
Slope (%) = (1 ÷ N) × 100. For 1:60 that is 1.67%; for 1:40, 2.5%.
Roof Angle
Angle = arctan(1 ÷ N). That gives about 0.95° at 1:60, 1.43° at 1:40 and 0.72° at 1:80.
How to Calculate Firring Quantity
Number of Firring Lines
Firring Lines = Ceiling(Roof Width ÷ Spacing) + 1
The width and spacing are converted to the same unit first (roof width in m or ft, spacing in mm or in). Rounding up keeps every gap at or below the spacing you entered, and the extra line closes off the far edge. For a 4 m wide roof at 600 mm spacing: 4,000 ÷ 600 = 6.67, round up to 7, then add 1 to give 8 lines. In imperial, a 20 ft width at 24 in spacing gives 240 ÷ 24 = 10, plus 1, which is 11 lines.
Total Linear Material and Waste
Base Material = Firring Lines × Roof Run
Material With Waste = Base Material × (1 + Waste ÷ 100)
Eight lines over a 6 m run need 48 m of firring. With the default 10% waste, that becomes 52.8 m. The right waste allowance depends on your stock lengths, cutting pattern and roof shape, so enter your own figure instead of treating 10% as fixed.
Why Run Length Matters
Total fall is directly proportional to the run. A 10 m run at 1:40 needs 250 mm of fall, so a 25 mm low end becomes a 275 mm high end. The same gradient over 3 m needs only 75 mm.
Falling across the shorter dimension reduces the high-end depth, but the drainage layout, outlets and roof edges decide which way the roof should fall, not the size of the firring. Confirm the fall direction and the construction depth available at both ends before calculating.
Firring vs Tapered Insulation
Firring creates the fall in the timber structure, so the deck itself slopes and insulation is added separately according to the roof build-up. Tapered insulation creates the fall within the insulation boards on a level deck, and has to be designed and installed as part of the manufacturer’s system. Both solve the same geometry problem, but the choice depends on the whole roof design, not just the calculated depth.
Common Firring Calculation Mistakes
- Using roof area instead of run. The fall depends only on the horizontal distance in the direction of fall.
- Mixing units. 6 m ÷ 60 is 0.1 m (100 mm), not 0.1 mm. Convert the run to the depth unit first.
- Forgetting the low-end depth. The total fall is not the high-end depth unless the low end is zero.
- Comparing width and spacing in different units. A 20 ft roof at 24 in spacing needs 11 lines, not 2.
- Confusing firring with furring. A furring strip quantity is not a tapered firring calculation.
- Assuming a fixed waste percentage. Waste varies with stock lengths and the cutting pattern.
Firring Calculator FAQs
Gradient and Fall Questions
How do you calculate firring?
Work out the total fall as Run ÷ N, with the run converted to the depth unit, then add the low-end depth to get the high-end depth.
How do I calculate a 1:60 fall?
Divide the run by 60 in the unit you want for the fall. A 6 m run gives 6,000 ÷ 60 = 100 mm. That works out to 16.67 mm per metre.
What is the fall for 1:40 and 1:80?
1:40 falls 25 mm per metre, so a 4 m run falls 100 mm. 1:80 falls 12.5 mm per metre, so the same run falls 50 mm.
Does a smaller ratio mean a steeper roof?
Yes. For the same run, 1:40 gives more fall than 1:80, so the high end of the firring is deeper.
Does the calculator tell me which gradient to use?
No. It calculates the geometry of the gradient you enter. The required gradient comes from the roof design, roofing system, drainage and applicable requirements.
Using the Calculator
How many firring strips do I need?
Use Calculate Firring Quantity. Lines = Ceiling(Width ÷ Spacing) + 1, with both in the same unit, and total material = lines × run.
Can I use feet and inches or metres and millimetres?
Yes. Imperial takes the run and width in feet and the depths, fall and spacing in inches. Metric uses metres and millimetres.
Can I enter a custom gradient?
Yes. Choose Custom and enter the N value of a 1:N ratio. For example, 70 gives 1:70.
Does the calculator include waste?
Yes, in quantity mode. It shows the base material, the waste allowance and the total including waste.
Is firring the same as furring?
Not usually. Firring is tapered to create a fall, while furring strips are generally uniform battens for spacing or fixing. Check the product and its application before ordering.
Before Ordering Firring
The calculator gives a geometric planning figure. Before ordering or installing, confirm:
- The drainage direction and outlet positions
- The roof covering or membrane system and its required finished fall
- The roof structure, joist direction and allowable deflection
- The construction depth available at upstands, parapets, openings and abutments
- Insulation requirements and the overall roof build-up
- Stock lengths, cutting and joining
- Structural design and the building requirements that apply to your project