Map and plan scale
real distance = map distance × n
The 1:n scale in the three directions of the problem: the real distance from a measurement on the map, the distance on the document from the ground, or the scale itself from a pair of distances. The line "one centimetre represents X metres" gives the quick reading of any document, from the 1:50 house plan to the 1:1,000,000 road map. Enlargements (2:1, mechanics and microscopy) are handled like reductions, and the note dismantles the area trap: areas follow n², not n.
1 km
- Calculation
- real = 4 cm × 25000 = 1 km
- One centimetre represents
- 250 m
This measurement represents 1 km on the ground.
Areas follow the square of the scale, not the scale: one square centimetre at 1:25,000 covers 6.25 hectares, at 1:50,000 it covers 25, four times more. Halving the scale halves the lengths and quarters the detail.
Quick map reading: at 1:25,000, 1 cm is 250 m and 4 cm is 1 km. In the field, measure on the map with the compass’s graduated edge or a calibrated blade of grass: thumb precision is enough, the reading error always dominates the scale error.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasreal distance = map distance × n
real distance = map distance × n
map distance = real distance / n
n = real distance / map distance (same unit)
areas: factor n²
A 1:n scale says one centimetre of the document represents n centimetres of the ground: the three calculations are the same equality read three ways. The only care is the unit: the ratio n compares two lengths expressed alike.
- Scale 1:n
- · the ratio between drawing and reality: 1 cm of the document is n cm of the ground. The larger n, the more the map covers and the less it details.
- Large and small scale
- · counter-intuitive: 1:25,000 is a LARGE scale (the ratio 1/25,000 is larger than 1/1,000,000), hence more detailed. The world map is small-scale.
- Enlargement
- · n below 1, written the other way round: 2:1 means a drawing twice the object. Precision mechanics, microscopy.
- Usual scales
- · 1:50 to 1:200 for building plans, 1:25,000 for hiking, 1:250,000 for driving, 1:1,000,000 and beyond for atlases.
Validity domainThe calculation is an exact ratio: all the uncertainty comes from the measurements, and on a map folded at the bottom of a bag, the millimetre of reading is worth 25 m at 1:25,000.
The calculation is an exact ratio: all the uncertainty comes from the measurements, and on a map folded at the bottom of a bag, the millimetre of reading is worth 25 m at 1:25,000. At very small scales (countries, continents), the map projection distorts distances: the displayed scale is exact only along certain lines, and no single ratio faithfully converts an atlas. For a real road route, the ground climbs and drops: the map gives the horizontal distance, see the slope tool for the true length.
The area trapThe scale is a ratio of lengths: areas, products of two lengths, follow its square.
The scale is a ratio of lengths: areas, products of two lengths, follow its square. One square centimetre at 1:25,000 covers 250 m × 250 m = 6.25 hectares; at 1:50,000, 25 hectares. That is why moving "one scale down" does not lose half the detail but three quarters: every symbol, every name must summarise four times more ground. And the same n² governs scale models: a 1:100 model weighs and costs by laws in n² and n³, never in n.
Reading the resultThe line "one centimetre represents X metres" is the reading key to memorise before leaving: 250 m at 1:25,000, 4 cm to the kilometre.
The line "one centimetre represents X metres" is the reading key to memorise before leaving: 250 m at 1:25,000, 4 cm to the kilometre. To recover the scale of a document without a title block (photocopy, old plan, screenshot), measure an element of known length, a 90 cm door on a plan, a football pitch, a street measurable online, and let the "unknown scale" mode take the ratio. Beware photocopies and resized PDFs: the printed scale lies as soon as the document has been rescaled.