This scale factor calculator works in both directions: give it two lengths and it finds the scale factor between them, or give it a factor and a measurement and it scales it. It handles ratio notation like 1:48, decimal factors, and imperial architect's scales such as quarter-inch to the foot. It also shows what happens to area and volume, which scale by the square and the cube rather than in step with length — the single most common mistake in scaling work.
Find a factor, scale a measurement, or read a real dimension straight off a drawing.
Units may differ between the two fields. That is the point: 15 cm on the model against 7.2 m on the building.
| Figure | Dimensions | Area multiplier | Volume multiplier |
|---|
A scale factor is the number every length gets multiplied by when something is resized. If a model is built at a scale factor of 0.02, every dimension of the real object is multiplied by 0.02 to get the model dimension. Nothing else changes — angles stay the same, proportions stay the same, only size moves.
It shows up written three different ways and they all mean the same thing. A decimal, 0.02. A ratio, 1:50. A fraction, 1/50. The calculator above accepts all three and shows all three, because different trades default to different notation — architects and modelmakers use ratios, maths classrooms use decimals and fractions, and engineering drawings sometimes use a verbal form like one inch to fifty feet.
Two objects related by a scale factor are described as similar. That word has a precise meaning in geometry: same shape, corresponding angles equal, corresponding sides in constant proportion. It is the formal version of the everyday idea that a photograph and its enlargement show the same thing at different sizes.
Divide the new length by the original length. That is the whole formula. The only thing to be careful about is which measurement counts as the original, because swapping them gives you the reciprocal — 2 instead of 0.5 — and both are correct answers to different questions.
Worked example. A model car measures 11 cm long and the real car is 4.4 m. Convert: 11 cm is 0.11 m. Divide: 0.11 / 4.4 = 0.025. As a ratio that is 1:40. Going the other way, if you know a model is 1:24 and it measures 19 cm, the real length is 19 x 24 = 456 cm, or 4.56 m.
A scale factor greater than 1 enlarges: the new object is bigger. A factor between 0 and 1 reduces. A factor of exactly 1 leaves the object unchanged, which sounds useless but is a real answer when you are checking whether two things are the same size.
Ratio notation is where confusion creeps in, because 1:48 and 48:1 are both valid and mean opposite things. The convention on drawings is that the first number refers to the drawing and the second to reality, so 1:48 means one unit on paper equals forty-eight units on the building — a reduction. A 48:1 drawing would be a magnified detail, which does happen on component drawings but is rare. When a ratio appears without context, assume the drawing convention.
Fractional factors are the same thing written differently. A scale factor of 3/4 is 0.75, a reduction to three quarters of the original size. A scale factor of 5/4 is 1.25, an enlargement. Neither is a ratio in the drawing sense and neither should be written 3:4 in that context, because that would read as a drawing scale.
This is the part that catches people out, and it catches them out in expensive ways. If you double every length, the area does not double — it quadruples. The volume does not double either; it goes up eight times. Length scales by k, area by k squared, and volume by k cubed.
The reason is straightforward once seen. Area is length times width, and both got multiplied by k, so the area gets multiplied by k twice over. Volume is length times width times height, so k applies three times. A 1:24 model of a building has one twenty-fourth the height but only one five-hundred-and-seventy-sixth of the floor area, and one thirteen-thousand-eight-hundred-and-twenty-fourth of the volume.
Practically: paint quantities, material costs and surface finishes follow the squared rule; concrete, fill, water and weight follow the cubed rule. Scaling a recipe or a tank or a foundation by "twice as big" without saying twice as big in what dimension is how estimates go badly wrong. The calculator above shows all three multipliers together for exactly this reason.
| Scale factor (k) | Area (× k²) | Volume (× k³) | Effect |
|---|---|---|---|
| 0.1 | 0.01 | 0.001 | Reduction |
| 0.25 | 0.0625 | 0.015625 | Reduction |
| 0.5 | 0.25 | 0.125 | Reduction |
| 0.75 | 0.5625 | 0.421875 | Reduction |
| 1 | 1 | 1 | Unchanged |
| 1.25 | 1.5625 | 1.953125 | Enlargement |
| 1.5 | 2.25 | 3.375 | Enlargement |
| 2 | 4 | 8 | Enlargement |
| 2.5 | 6.25 | 15.625 | Enlargement |
| 3 | 9 | 27 | Enlargement |
| 4 | 16 | 64 | Enlargement |
| 5 | 25 | 125 | Enlargement |
| 10 | 100 | 1000 | Enlargement |
In a maths classroom the same idea is called a dilation. A shape is dilated about a centre point by a scale factor, producing an image that is similar to the original. Every point moves along the line from the centre through that point, ending up k times as far from the centre as it started.
The vocabulary differs from the drawing world but the arithmetic is identical. The original is the pre-image, the result is the image, and the scale factor is image length divided by pre-image length. A dilation with k greater than 1 is an enlargement, k between 0 and 1 a reduction, and k = 1 leaves the figure fixed. Some courses also treat negative scale factors, which rotate the image 180 degrees about the centre as well as resizing it.
For similar triangles and other similar polygons the practical test is that corresponding sides share a constant ratio and corresponding angles are equal. If you are given two similar figures and asked for a missing side, find the scale factor from any pair of corresponding sides you do know, then apply it. That is the entire method, and the calculator above will do the division for you.
| Pre-image side | Image side | Scale factor | Type |
|---|---|---|---|
| 4 | 12 | 3 | Enlargement |
| 5 | 15 | 3 | Enlargement |
| 6 | 9 | 1.5 | Enlargement |
| 8 | 10 | 1.25 | Enlargement |
| 10 | 10 | 1 | Congruent |
| 12 | 9 | 0.75 | Reduction |
| 16 | 12 | 0.75 | Reduction |
| 20 | 5 | 0.25 | Reduction |
| 9 | 6 | 0.667 (2/3) | Reduction |
| 7 | 17.5 | 2.5 | Enlargement |
The most common real task is the reverse of what most calculators offer. You have a plan, a ruler and a stated scale, and you want to know how long something actually is. Measure the length on the drawing, multiply by the scale denominator, and convert units.
A line measuring 45 mm on a 1:20 drawing represents 45 x 20 = 900 mm, or 0.9 m. On a 1:50 drawing the same 45 mm line would be 2.25 m. This is why misreading the title block is such an expensive mistake — the measurement is right and the answer is still wrong by a factor of two and a half.
Imperial architectural drawings work the same way once the scale is expressed as a ratio. A quarter-inch-to-the-foot drawing is 1:48, so 3.5 inches measured on paper is 3.5 x 48 = 168 inches, which is 14 feet. The tables below give the ratio for every standard architect and engineer scale so the conversion is a lookup rather than a calculation.
| Measured on drawing | Real at 1:48 | Real at 1:100 | Real at 1:20 |
|---|---|---|---|
| 1 mm | 0.048 m | 0.10 m | 0.02 m |
| 2 mm | 0.096 m | 0.20 m | 0.04 m |
| 5 mm | 0.240 m | 0.50 m | 0.10 m |
| 10 mm | 0.480 m | 1.00 m | 0.20 m |
| 15 mm | 0.720 m | 1.50 m | 0.30 m |
| 20 mm | 0.960 m | 2.00 m | 0.40 m |
| 25 mm | 1.200 m | 2.50 m | 0.50 m |
| 30 mm | 1.440 m | 3.00 m | 0.60 m |
| 40 mm | 1.920 m | 4.00 m | 0.80 m |
| 50 mm | 2.400 m | 5.00 m | 1.00 m |
| 60 mm | 2.880 m | 6.00 m | 1.20 m |
| 75 mm | 3.600 m | 7.50 m | 1.50 m |
| 100 mm | 4.800 m | 10.00 m | 2.00 m |
| 125 mm | 6.000 m | 12.50 m | 2.50 m |
| 150 mm | 7.200 m | 15.00 m | 3.00 m |
| 200 mm | 9.600 m | 20.00 m | 4.00 m |
| 250 mm | 12.000 m | 25.00 m | 5.00 m |
| 300 mm | 14.400 m | 30.00 m | 6.00 m |
| 350 mm | 16.800 m | 35.00 m | 7.00 m |
| 400 mm | 19.200 m | 40.00 m | 8.00 m |
| 500 mm | 24.000 m | 50.00 m | 10.00 m |
| 600 mm | 28.800 m | 60.00 m | 12.00 m |
| 750 mm | 36.000 m | 75.00 m | 15.00 m |
| 1000 mm | 48.000 m | 100.00 m | 20.00 m |
Every scale expressed as a ratio, a decimal factor, and its reciprocal. The reciprocal column is there because it is what you multiply a drawing measurement by to get the real dimension.
| Ratio | Decimal factor | Reciprocal | Multiply drawing length by |
|---|---|---|---|
| 1:1 | 1 | 1:1 | 1 |
| 1:2 | 0.5 | 2:1 | 2 |
| 1:3 | 0.33333 | 3:1 | 3 |
| 1:4 | 0.25 | 4:1 | 4 |
| 1:5 | 0.2 | 5:1 | 5 |
| 1:6 | 0.16667 | 6:1 | 6 |
| 1:8 | 0.125 | 8:1 | 8 |
| 1:10 | 0.1 | 10:1 | 10 |
| 1:12 | 0.08333 | 12:1 | 12 |
| 1:16 | 0.0625 | 16:1 | 16 |
| 1:20 | 0.05 | 20:1 | 20 |
| 1:24 | 0.04167 | 24:1 | 24 |
| 1:25 | 0.04 | 25:1 | 25 |
| 1:30 | 0.03333 | 30:1 | 30 |
| 1:32 | 0.03125 | 32:1 | 32 |
| 1:36 | 0.02778 | 36:1 | 36 |
| 1:40 | 0.025 | 40:1 | 40 |
| 1:48 | 0.02083 | 48:1 | 48 |
| 1:50 | 0.02 | 50:1 | 50 |
| 1:64 | 0.01563 | 64:1 | 64 |
| 1:72 | 0.01389 | 72:1 | 72 |
| 1:75 | 0.01333 | 75:1 | 75 |
| 1:87 | 0.01149 | 87:1 | 87 |
| 1:96 | 0.01042 | 96:1 | 96 |
| 1:100 | 0.01 | 100:1 | 100 |
| 1:144 | 0.00694 | 144:1 | 144 |
| 1:150 | 0.00667 | 150:1 | 150 |
| 1:160 | 0.00625 | 160:1 | 160 |
| 1:192 | 0.00521 | 192:1 | 192 |
| 1:200 | 0.005 | 200:1 | 200 |
| 1:220 | 0.00455 | 220:1 | 220 |
| 1:250 | 0.004 | 250:1 | 250 |
| 1:300 | 0.00333 | 300:1 | 300 |
| 1:500 | 0.002 | 500:1 | 500 |
| 1:1000 | 0.001 | 1000:1 | 1000 |
| 1:1250 | 0.0008 | 1250:1 | 1250 |
| 1:2500 | 0.0004 | 2500:1 | 2500 |
The imperial architect scale expresses how many inches on paper represent one foot in reality. Converting to a ratio just means putting both sides in the same unit: a quarter inch to twelve inches is 1:48. If the unit conversion itself is the sticking point, our inches to feet converter handles the imperial side.
| Architect scale | Ratio | Decimal factor | Meaning |
|---|---|---|---|
| 3" = 1'-0" | 1:4 | 0.25 | 1" on paper = 0.333 ft |
| 1-1/2" = 1'-0" | 1:8 | 0.125 | 1" on paper = 0.667 ft |
| 1" = 1'-0" | 1:12 | 0.083333 | 1" on paper = 1 ft |
| 3/4" = 1'-0" | 1:16 | 0.0625 | 1" on paper = 1.333 ft |
| 1/2" = 1'-0" | 1:24 | 0.041667 | 1" on paper = 2 ft |
| 3/8" = 1'-0" | 1:32 | 0.03125 | 1" on paper = 2.667 ft |
| 1/4" = 1'-0" | 1:48 | 0.020833 | 1" on paper = 4 ft |
| 3/16" = 1'-0" | 1:64 | 0.015625 | 1" on paper = 5.333 ft |
| 1/8" = 1'-0" | 1:96 | 0.010417 | 1" on paper = 8 ft |
| 3/32" = 1'-0" | 1:128 | 0.007813 | 1" on paper = 10.667 ft |
| 1/16" = 1'-0" | 1:192 | 0.005208 | 1" on paper = 16 ft |
| 1/32" = 1'-0" | 1:384 | 0.002604 | 1" on paper = 32 ft |
Engineer scales run in round numbers of feet to the inch and are used for site plans, civil drawings and surveys rather than building details. If your survey work also involves coordinates in degrees, the degrees minutes seconds calculator covers that side.
| Engineer scale | Ratio | Decimal factor | Meaning |
|---|---|---|---|
| 1" = 10' | 1:120 | 0.00833333 | 1" on paper = 10 ft |
| 1" = 20' | 1:240 | 0.00416667 | 1" on paper = 20 ft |
| 1" = 30' | 1:360 | 0.00277778 | 1" on paper = 30 ft |
| 1" = 40' | 1:480 | 0.00208333 | 1" on paper = 40 ft |
| 1" = 50' | 1:600 | 0.00166667 | 1" on paper = 50 ft |
| 1" = 60' | 1:720 | 0.00138889 | 1" on paper = 60 ft |
| 1" = 80' | 1:960 | 0.00104167 | 1" on paper = 80 ft |
| 1" = 100' | 1:1200 | 0.00083333 | 1" on paper = 100 ft |
Metric practice uses preferred ratios rather than unit-to-unit statements, which makes the arithmetic simpler — the denominator is the number you multiply by.
| Scale | Typical use | Decimal factor |
|---|---|---|
| 1:1 | Full size detail | 1 |
| 1:2 | Large component detail | 0.5 |
| 1:5 | Component detail | 0.2 |
| 1:10 | Construction detail | 0.1 |
| 1:20 | Room and joinery detail | 0.05 |
| 1:50 | Floor plan, section | 0.02 |
| 1:100 | Building plan, elevation | 0.01 |
| 1:200 | Large building, site plan | 0.005 |
| 1:500 | Site and block plan | 0.002 |
| 1:1000 | Site location plan | 0.001 |
| 1:1250 | Urban location plan (UK) | 0.0008 |
| 1:2500 | Rural location plan (UK) | 0.0004 |
Model scales are conventions rather than standards, and several disciplines have settled on different numbers for historical reasons. Model railway gauges in particular carry letter names that map to specific ratios, and the British and American versions of the same letter sometimes differ.
| Scale | Name or gauge | Field | 1 m real = |
|---|---|---|---|
| 1:8 | — | Large display models, engines | 125 mm |
| 1:12 | Dollhouse (1 inch) | Dollhouses, guitars | 83.3 mm |
| 1:18 | — | Diecast cars | 55.6 mm |
| 1:22.5 | G gauge | Garden railway | 44.4 mm |
| 1:24 | Half-inch dollhouse | Diecast, dollhouse | 41.7 mm |
| 1:32 | No. 1 gauge | Diecast, aircraft, figures | 31.3 mm |
| 1:35 | — | Military vehicles | 28.6 mm |
| 1:43.5 | O gauge (UK/EU) | Model railway, diecast | 23 mm |
| 1:48 | O scale (US) | Model railway, aircraft | 20.8 mm |
| 1:64 | S scale | Model railway, diecast | 15.6 mm |
| 1:72 | — | Aircraft, military | 13.9 mm |
| 1:76.2 | OO gauge | British model railway | 13.1 mm |
| 1:87.1 | HO scale | Model railway (worldwide) | 11.5 mm |
| 1:100 | — | Architectural models | 10 mm |
| 1:120 | TT scale | Model railway | 8.3 mm |
| 1:144 | — | Aircraft | 6.9 mm |
| 1:148 | N gauge (UK) | British model railway | 6.8 mm |
| 1:160 | N scale | Model railway | 6.3 mm |
| 1:200 | — | Aircraft, architecture | 5 mm |
| 1:220 | Z scale | Model railway | 4.5 mm |
| 1:285 | 6mm | Wargaming | 3.5 mm |
| 1:350 | — | Ship models | 2.9 mm |
| 1:450 | T scale | Model railway | 2.2 mm |
| 1:700 | — | Ship models | 1.4 mm |
Map scales are ratios like any other, but the denominators are large enough that the useful question is usually how much ground one centimetre or one inch covers.
| Scale | 1 cm on map = | 1 inch on map = | Typical series |
|---|---|---|---|
| 1:10,000 | 100 m | 833 ft | Detailed urban mapping |
| 1:24,000 | 240 m | 2,000 ft | USGS 7.5-minute quadrangle |
| 1:25,000 | 250 m | 2,083 ft | OS Explorer (UK) |
| 1:50,000 | 500 m | 4,167 ft | OS Landranger (UK) |
| 1:62,500 | 625 m | 5,208 ft | Older USGS 15-minute |
| 1:63,360 | 634 m | 1 mile (exact) | One inch to the mile |
| 1:100,000 | 1 km | 1.58 mi | Regional mapping |
| 1:250,000 | 2.5 km | 3.95 mi | Road and regional atlas |
| 1:500,000 | 5 km | 7.89 mi | Aeronautical charts |
| 1:1,000,000 | 10 km | 15.78 mi | International world series |
Scale factor is standard geometry coursework and it is assessed on method: find the factor from a known pair of corresponding sides, then apply it to the unknown. The dilation table and the area/volume panel are built for that work, including the fractional and 2.5 factors that turn up most often in exercises.
Converting between drawing measurements and real dimensions, and moving between imperial architect scales and metric ratios. The Read a Drawing tab and the architectural and engineering tables exist for this, and the ratio-recognition feature names the scale when you land on a standard one.
Working out a component size for a given scale, or identifying what scale an existing model is by measuring a known feature. The model scale table lists what one real metre becomes at every common ratio, which is the direction modellers actually need.
The squared and cubed rules decide quantities. Surface treatments follow area, so they scale by k squared; fill, concrete and weight follow volume, so they scale by k cubed. Getting this wrong is the difference between an accurate estimate and one that is out by an order of magnitude.
Resizing artwork, prints and images while keeping proportions. A scale factor applied to both dimensions preserves the aspect ratio; applying it to one only does not, which is the arithmetic behind every distorted image.
Divide the new length by the original length, after converting both to the same unit. A 12 cm original becoming 60 cm gives a scale factor of 5. Choosing which measurement is the original matters, because swapping them gives you the reciprocal.
A scale factor of 2.5 is an enlargement: every length becomes two and a half times longer. Area becomes 6.25 times larger, since 2.5 squared is 6.25, and volume becomes 15.625 times larger, since 2.5 cubed is 15.625.
A scale factor of 3/4, or 0.75, is a reduction — every length becomes three quarters of its original. Area is reduced to 0.5625 of the original (0.75 squared) and volume to 0.421875 (0.75 cubed).
A 1:20 scale means one unit on the drawing represents twenty units in reality, so it is a reduction with a scale factor of 0.05. A line measuring 45 mm on a 1:20 drawing represents 900 mm, or 0.9 m, in real life.
No — area scales by the square of the factor. Doubling every length multiplies area by four and volume by eight. This catches people out constantly when estimating paint, material or fill quantities from a scaled drawing.
It means one unit on paper equals forty-eight in reality, a scale factor of about 0.0208. In imperial terms it is the quarter-inch-to-the-foot architect scale, and it is also O scale in American model railways.
It is 1:48. A quarter of an inch on paper represents twelve inches in reality, and 0.25 divided by 12 is 1/48. Every imperial architect scale converts the same way — divide the paper inches by twelve.
Measure the length on the drawing and multiply by the scale denominator. On a 1:50 drawing, 45 mm measured becomes 45 x 50 = 2,250 mm, or 2.25 m. The Read a Drawing tab above does this with the standard scales pre-loaded.
They express the same relationship in different notation. A scale factor is a single multiplier such as 0.02; a ratio writes it as a comparison such as 1:50. Ratios are conventional on drawings and models, decimals in maths and in code.
A factor of 1 leaves the figure unchanged, which is a valid answer when checking whether two objects are the same size. Negative factors appear in geometry courses and mean the image is rotated 180 degrees about the centre of dilation as well as resized.
HO is 1:87.1, usually quoted as 1:87, so one real metre becomes about 11.5 mm. British OO gauge is 1:76.2 and looks noticeably larger despite running on the same track gauge, which is a long-standing quirk of the hobby.
We built the Scale Factor Calculator because every competing page converts one length and stops: nothing reads a drawing backwards, nothing warns you that area scales by the square, and nothing tells you 1:48 has a name. This one does all three, with the architectural, model and map scale charts built in. This site is a part of the ads4good Network.
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