Building maths, worked through
Guides to the numbers on site: squaring frames, stairs, concrete, decking, framing and levels. Millimetres first, every example worked out, and each one checked against the calculator in MeisterCalc that does it.
Stairs
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How many steps do I need for a 2.7 m or 3 m floor height?
A 2.7 m floor height takes 15 risers of 180 mm. A 3 m floor height takes 17 risers of 176.5 mm. Worked sums for 2.4, 2.7, 3 m and 10 ft.
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What is the 2R + G stair formula, and how do I use it?
2R + G is twice the riser plus the going. About 600 mm is a comfortable step. Worked for 240, 260 and 300 mm goings on a 2.7 m rise.
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How big does a stairwell opening need to be?
Opening length = (floor thickness + headroom) × going ÷ rise: 2933 mm for 200 mm of floor and 2000 mm headroom. Worked steps and the code figures.
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How do I fit a staircase into a fixed length?
Divide the fixed run into equal goings, then check rise, going and 2R + G. 2700 mm of rise in 2800 mm of run fails Australian limits; 13 risers fit England's.
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What is the going of a stair, and how is it different from the tread?
The going is the distance from one stair nosing to the next. It equals the tread depth less any overlap. Worked example and minimums included.
Balusters, pickets and railings
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What is the maximum gap between balusters in Australia?
In Australia a balustrade opening must not let a 125 mm sphere pass (NCC Housing Provisions 11.3.4). Heights, the 40 mm edge gap and a worked layout.
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What is the maximum gap between stair spindles in the UK?
In England a 100 mm sphere must not pass through stair guarding where under-fives are present. Approved Document K paragraphs and a spindle layout.
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What is the maximum gap between balusters in New Zealand?
NZ barriers must stop a 100 mm sphere passing, under F4/AS1. Here is what that means for baluster gaps, with a worked layout and the clause linked.
Squaring and setting out
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How do I check if a frame is square?
Measure both diagonals. If opposite sides match and the diagonals are equal, the frame is square. Here's the target diagonal and how far to push if not.
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How do I use the 3-4-5 rule to set out a right angle?
Mark 3 units along one line and 4 along the other from the same corner. When the gap between the marks reads 5, the corner is 90 degrees. Metric sizes.
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How do I square a deck frame?
Square the outer frame before the joists: measure both diagonals, push the long one in by half the gap, brace it and re-measure. Worked example in mm.
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How do I set out a building or slab square?
Fix string lines on profiles, square one corner with a 3-4-5 triangle, then check both diagonals. Worked target diagonals in mm and how far to move.
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How do you calculate the diagonal of a rectangle for a frame or slab?
Diagonal = √(length² + width²). A 4800 × 3600 mm frame measures 6000 mm corner to corner. Worked in mm, with how to tape it on site.
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How far out of square is acceptable for a deck, shed or frame?
There is no single number. Here is how to read the racking gap, what 12 mm means on a 4.8 m frame, and how to decide what the next job can live with.
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What should the diagonal be to square up a frame, and which way do I push?
Free square-up calculator in mm: the diagonal a square frame should measure, and from two measured diagonals, how far out it is and which corners to push.
Roof pitch, slope and fall
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How do I calculate roof pitch in degrees?
Divide rise by run, then take the arctan: 1500 mm over 4000 mm is 20.6°. Worked metric examples, a conversion table and how to measure it on site.
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What is a roof pitch in degrees? (X/12 and 1:X conversion chart)
Roof pitch in degrees is arctan(rise ÷ run). 4/12 is 18.43°, 6/12 is 26.57° and 12/12 is 45°. Full X/12, 1:X and per cent chart, with the formula.
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How do I convert a slope percentage to degrees (or a 1 in X ratio)?
Degrees = arctan(slope % ÷ 100). 10% is 5.71°, 1 in 12 is 8.33% or 4.76°. One chart of %, 1 in N, degrees and mm per metre.
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How much fall is 1 in 100 (and 1 in 60, 1 in 80) in millimetres?
1 in 100 is 10 mm per metre, 1% or 0.573 degrees: 50 mm over 5 m. Fall tables for 1 in 40 to 1 in 500 over 1 to 10 m, with sourced rules.
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How long does a 1 in 14 ramp need to be?
A 1 in 14 ramp runs 14 mm per 1 mm of rise: 150 mm needs 2.1 m. It is 7.14% or 4.09 degrees. Table, worked example and sourced rules.
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How do I calculate rafter length from the pitch and span?
Rafter line length = run ÷ cos(angle). Add the horizontal overhang to the run first. Worked in mm: 8000 span, 22.5°, 450 overhang = 4817 mm.
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How do I work out the gradient of a driveway?
Driveway gradient = rise ÷ run × 100. A 840 mm fall over 6 m is 14%, 1 in 7.14 or 7.97°. How to measure it, with sourced Australian limits.
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Is there a roof pitch calculator app that solves from any two values?
MeisterCalc's Pitch calculator on Android solves rise, run, angle, % grade and X/12 from any two. Metric first, works offline. It is a paid calculator.
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How do you calculate ridge or gable height from span and pitch?
Ridge height above the wall plate = half the span × tan(pitch). 8000 mm at 22.5° gives 1657 mm. Gable, skillion and reverse sums, in metric.
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How much fall should a patio or slab have away from the house?
Fall the patio away from the house. Australia's NCC grades the first metre at 25 or 50 mm; UK guidance is 1 in 60. Here is what that is over 3, 4 and 5 m.
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What is the minimum fall for a gutter?
In Australia an eaves gutter needs a fall of not less than 1:500 (NCC 2022): 2 mm per metre, 12 mm over 6 m. Fall table, string-line heights and limits.
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What fall does a drainage pipe need, in mm over its length?
Drainage pipe fall is the run divided by N: 1 in 40 over 8 m is 200 mm. Sourced England minimums, the far-end invert level and how to check it.
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How do you calculate the gradient of a ramp?
Ramp gradient is rise ÷ run. Worked examples for the ratio (1 in N), percentage and degrees, how to measure a ramp on site, and what the rules say.
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How do I convert a fall between 1 in X, %, degrees and mm per metre?
Free fall calculator: convert a fall between 1 in X, %, degrees and mm per metre, get the drop over any run, and see common falls with official sources.
Levels and surveying
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How do I use a dumpy level and staff on site?
Level the instrument, read the staff on a benchmark to get the height of instrument, then subtract each reading for that point's level. Worked example.
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How do I calculate a reduced level (RL) from staff readings?
HI = benchmark RL + backsight; RL = HI − foresight. Worked examples line by line, including a negative RL and rise and fall.
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How do I measure the slope of a block of land?
Slope of land = fall ÷ horizontal distance. Get the fall from two levels, then write it as %, 1 in X or degrees. Worked example: 0.84 m over 24 m.
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How do you read a dumpy level staff?
Read the number below the crosshair, count the 10 mm blocks, estimate the millimetre, and write it in metres. Worked readings and the sums.
Wall framing
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How do I work out the framing for a stud wall?
Work a stud wall in order: stud length, stud count, lineal metres, plates, noggings, openings and marks. Metric, with a 3.6 m wall worked through.
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How many studs do I need for a wall?
Divide wall length by stud spacing, round up, add one. A 3.6 m wall needs 9 studs at 450 mm centres or 7 at 600 mm. Includes a table and lineal metres.
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How do I mark out studs at 450 or 600 centres?
Hook the tape at the plate end and mark every stud off that one reading. Marks at 450 and 600 mm centres, worked through from a 38 mm end stud.
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What is the standard stud spacing in Australia?
Stud spacing in Australia is set by the framing design, not one number. 450 and 600 mm are common centres. What decides it and where to look.
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What stud spacing should I use for a stud wall in the UK?
Stud spacing in the UK is set by the plasterboard maker's guide or the structural design, not one rule. What decides it, and how to count studs.
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What is the stud spacing under NZS 3604?
No NZS 3604 stud spacing is quoted here: it depends on the wall. Where to read the standard, what moves the figure, and how to count studs.
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How many joists do I need for a deck or floor?
Divide the length by the joist spacing, round up, add one. A 4.8 m deck needs 12 joists at 450 mm centres or 9 at 600 mm. Includes lineal metres.
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Is there a framing calculator app for studs, layout marks and raked walls?
Yes, on Android. MeisterCalc counts studs, gives layout marks and works out raked walls, metric first. No roof framing or openings. Free tier explained.
Even spacing and fence posts
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How do I divide a length into equal spaces?
Divide the length by the spacing you want, round to whole spaces, divide again for the exact gap, add one for the marks: 5500 mm is 12 spaces of 458.3 mm.
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How many fence posts do I need, and how far apart should they be?
Posts = bays + 1. Divide the run by the maker's maximum, round up, then space evenly: a 10 m run at 2.4 m maximum is 5 bays and 6 posts.
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Is there an equal spacing calculator app for posts, studs and pickets?
Yes. MeisterCalc for Android splits a length into equal spaces and gives the gap and post count. Worked example, which tool to use, and the limits.
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How do you space deck posts evenly?
Divide the centre-to-centre length by the maximum spacing, round up to whole bays, then divide equally. Posts = bays + 1. A worked metric example.
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How many fence panels do I need for a run?
Divide the run by panel width plus one post width, round down, add one post. Worked in mm and feet, with what to do about the short bay left over.
Decking
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How many decking boards (lineal metres) do I need?
Divide deck width by board width plus gap, round up, then multiply by length. Worked example: 6 m × 4 m deck, 90 mm boards, 258 m, order 283.8 m.
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How many lineal metres of decking are in a square metre?
No single factor: lineal metres per m² = 1000 ÷ (board face + gap in mm). 90 mm boards at a 5 mm gap give 10.53 m per m². Table inside.
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How big should the gap between decking boards be?
Timber decking gaps are 2 to 5 mm at installation, by species, width and moisture. See the table, how the gap changes your order and how to fit whole boards.
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Is there a decking calculator app that works in lineal metres?
Yes: MeisterCalc's Decking calculator on Android gives boards across and lineal metres in mm. Worked example: 6 x 4 m, 258 m, order 283.8 m.
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The last deck board is too narrow: how do I avoid or fix it?
Do the sum before you lay: width minus whole boards and gaps. Then spread the leftover across the gaps or rip both edge boards equally. Worked in mm.
Concrete
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How much concrete do I need for a slab?
Multiply length × width × depth in metres, then add 10%. A 4 × 3 m slab, 100 mm deep, is 1.20 m³: order 1.32 m³. Size table and ready-mix vs bags.
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How much concrete do I need for a post hole?
A 300 mm wide, 800 mm deep post hole takes about 0.057 m³ (57 litres). Here is the formula, a size table and how to turn it into bags.
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How many 20 kg bags of concrete make a cubic metre?
Boral Concrete Mix 20 kg: 108 bags per m³. Cement Australia PROStrength 20 kg: about 110. Six makers' yields compared, the sum and a worked job.
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How much concrete do I need for strip footings?
Multiply the centreline length by the width and depth, then add about 10%. A 36 m run, 600 x 300 mm, is 6.48 m³, so order about 7.13 m³.
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Is there a free concrete calculator app for slabs and post holes?
Yes. MeisterCalc's Concrete calculator is free on Android: slab and post-hole volume in m³ and litres, plus 10% to order. It works offline.
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How much extra concrete should I order?
Add about 10% to the exact volume, 5% for a neat job and more on rough ground. A 1.20 m³ slab becomes 1.32 m³. Why, and how minimum loads work.
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How much does a cubic metre of concrete weigh?
A cubic metre of concrete weighs about 2.4 tonnes (2,400 kg). Half a cubic metre is about 1.2 t. Ask your supplier for your mix.
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How much screed do I need for a floor?
Screed volume is floor area × depth, plus 5 to 10%. A 20 m² floor at 65 mm is 1.30 m³, so order about 1.43 m³. Depth comes from the screed type.
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How do you calculate cubic metres (and convert mm to m3)?
Cubic metres = length × width × depth, all in metres. Divide millimetres by 1,000 first. Worked examples for slabs, rooms, holes and trenches.
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How do you convert square metres to cubic metres?
You can't convert them: multiply the area in m² by the depth in metres. 12 m² at 100 mm deep is 1.2 m³. Depth table and the reverse sum.
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How many cubic metres of concrete do I need for a slab, footing or post holes?
Free concrete calculator in m³ for slabs, strip footings and post holes: litres, an order figure with 10% extra, and bag counts from makers' data sheets.
Gravel, soil and asphalt
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How do I convert cubic metres to tonnes for gravel, soil and sand?
Tonnes = cubic metres × density in kg/m³ ÷ 1,000. Use your supplier's density, because loose, wet and compacted loads weigh differently.
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How much gravel do I need (in tonnes)?
Tonnes = length × width × depth (m) × density ÷ 1,000. Worked example, tonnes per square metre and a driveway with two layers.
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How much soil or topsoil do I need?
Soil in m³ = length × width × depth (m); tonnes = m³ × density ÷ 1,000. Worked raised bed, coverage per m³ and a lawn top-dress.
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How much asphalt (tarmac) do I need for a driveway?
Tonnes = length × width × compacted thickness (m) × density ÷ 1,000. Worked 10 m × 3 m driveway, tonnes per m², tarmac vs asphalt, and the base.
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How much road base (or Type 1) do I need?
Tonnes = length × width × compacted depth (m) × density ÷ 1,000. Worked patio example, tonnes per m², loose vs compacted, and UK Type 1.
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Is there a gravel, soil and asphalt calculator app that gives tonnes?
MeisterCalc has Gravel, Soil and Asphalt calculators for Android. Enter length, width, depth and density to get cubic metres, tonnes and an order figure.
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How much sand do I need for paving?
Tonnes = length × width × bedding depth (m) × density ÷ 1,000. Worked patio example, tonnes per m² and what to ask the supplier.
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How do you calculate the volume of a trench and the gravel or backfill for it?
Trench volume is length × width × depth in metres. A 10 m trench 0.6 m wide and 0.9 m deep is 5.4 m³, or 8.1 tonnes of gravel at 1,500 kg/m³.
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How many square metres does a tonne of gravel cover?
One tonne covers about 13 m² at 50 mm deep and 1,500 kg/m³. Table by depth and density, the formula, bulk bags and cubic metres.
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How many bulk bags of gravel do I need?
Bags = order tonnes ÷ the bag weight on your supplier's listing, rounded up. Worked example, coverage per bag at 25 to 100 mm and common mistakes.
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How many cubic metres does a trailer or box trailer hold?
A 6x4 box trailer holds about 0.7 m³ level full, but its weight limit usually caps a gravel load near 0.25 to 0.35 m³. Here is the sum.
Right-angle maths
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How do builders use Pythagoras on site?
Builders use Pythagoras to turn two sides of a right-angled triangle into the third: frame diagonals, stringers, rafters and braces. Worked in mm.
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How long should a knee brace be on a pergola?
Knee brace length is the diagonal of the drop and run: 600 mm legs at 45° give 848.5 mm. How to work it out, mark it and cut the ends, in mm.
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How far should a ladder be from the wall (the 1-in-4 rule)?
Put the foot of a straight ladder 1 m out for every 4 m of height, about 76 degrees. Worked heights in metres, the angle, and what the rule leaves out.
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What does a right angle triangle calculator in mm solve?
Give a right angle triangle calculator any two of base, rise, hypotenuse or an angle and it returns the rest in mm. Nine pairs, with worked numbers.
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How do you measure an angle with a tape measure?
Mark equal lengths on both edges, measure the gap between the marks, then read the angle from a table. 1000 mm marks and a 1414 mm gap is 90 degrees.
Metric and imperial
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How do I convert millimetres to feet, inches and sixteenths?
Divide mm by 25.4, split off feet, multiply the leftover by 16 and round. 1000 mm is 3' 3 3/8". Method, carry rule, building-size chart and error.
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Is there a construction calculator that works in millimetres?
Yes. MeisterCalc works in millimetres by default, with feet, inches and fractions one setting away. See what changes in each mode, with worked examples.
Choosing a construction calculator app
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What is the best construction calculator app for Android?
Twelve Android apps compared on units, calculators named, price model, offline use and ads, each fact linked to its source and checked on 29 October 2026.
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What are the alternatives to Construction Master Pro on Android?
Nine apps compared with Construction Master Pro on rafters, feet-inch maths, metric, price model and offline use, with sources and where each is stronger.
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Which construction calculator apps can you buy once, without a subscription?
Which Android construction calculator apps offer a one-time payment, what stays free, and what a lifetime unlock covers, from each listing, checked on 29 October 2026.
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Is there a free construction calculator app for Android?
Yes. MeisterCalc's Concrete, Stairs and Check Square calculators are free to use. The other 12 need a 3-day trial or a lifetime unlock. Android only.