Convert km to cm

Kilometres are the road distance nearly everywhere outside the United States and the United Kingdom, which is why converting them is usually about reading a map or a race entry.

Centimetres are the everyday metric length — body measurements, paper, furniture — and they are the one metric unit that has no direct customary counterpart, which is why so much converting happens through them.

Going from kilometres to centimetres moves the decimal point 5 places to the right and changes nothing else. There is no factor to remember and no rounding to decide: the digits stay in the same order and only their position changes.

1,234 km is 123400000 cm — same digits, moved along. That is worth knowing because it is the one kind of conversion you can check at a glance: if the digits of the answer are not the digits you started with, something other than the conversion has happened to them.

kilo- and centi- are not part of the unit — they are a multiplier bolted onto the front of it, and the same one means the same thing on every unit it appears on.

Here that is a thousand metres against a hundredth of a metre: 5 powers of ten apart, and the unit underneath both of them is the same metre. Nothing about the quantity changes — only how many of it you are counting in one go.

A kilometre is a hundred thousand centimetres, and on its own that is a figure with no application: nothing is drawn at full size at that scale. The number becomes useful only once it is divided by a ratio, and the arithmetic is always the same — a hundred thousand divided by the second number in the ratio gives the centimetres a kilometre occupies on the sheet.

That single operation covers the whole of drawing setup. At 1:1,000 a kilometre is 100 cm, at 1:2,500 it is 40 cm, at 1:10,000 it is 10 cm. Choosing a scale is therefore choosing how much paper a kilometre is worth, and the choice is usually made backwards: measure the sheet, decide how much ground has to appear on it, and pick the nearest standard ratio that fits.

Standard drawing sheets halve down a fixed series, so the sizes are known before the scale is chosen: A0 is 1189 × 841 mm, A1 is 841 × 594 mm, A2 is 594 × 420 mm. An A1 sheet is a little over 84 cm across its long side, which means a kilometre at 1:1,000 will not fit on it and the same kilometre at 1:1,250 will, with a few centimetres to spare for a title block and a margin.

Work the constraint in that order and the scale chooses itself. Take the longest ground dimension in kilometres, convert to centimetres, and divide by the usable width of the sheet after margins; the result is the smallest ratio that works, and the standard scale immediately below it is the one to draw at. Choosing a scale first and discovering the fit afterwards is how drawings end up spanning two sheets.

Planning and property work runs on a small set of ratios, and knowing what a kilometre becomes at each one makes an unfamiliar drawing legible immediately. A location plan is commonly 1:1,250 in a built-up area or 1:2,500 in open country, putting a kilometre at 80 cm and 40 cm respectively. A block plan is typically 1:500, at which a kilometre is two metres and only a fraction of it will appear.

The corresponding check is to find something on the sheet whose real size you know and measure it. A domestic house frontage is around 8 m, which is 6.4 mm at 1:1,250 and 3.2 mm at 1:2,500 — small, but distinguishable with a ruler. If the measurement does not match the stated ratio, the sheet has been resized and everything measured off it will be out by the same proportion.

Model railway scales make the impossibility of scale distance obvious. HO is 1:87, so a kilometre of prototype line is about 11.5 m of model, and even that is one of the larger common scales. At 1:148 or 1:160 the same kilometre is roughly seven metres, which is a generous room, and modellers building a route of several kilometres are working in tens of metres of track they do not have.

The answer the hobby settled on is to scale the objects and not the gaps. Buildings, rolling stock and figures are made to the ratio, while the distance between two stations is whatever the baseboard allows — a practice called selective compression. It is the same decision a cartographer makes when a road is drawn wider than scale so that it remains visible, and for the same reason.

Scaling down is unforgiving at the small end, and it is where a chosen ratio reveals whether it is workable. An adult of about 180 cm becomes roughly 2 cm at 1:87 and about 1.2 cm at 1:148. A mature tree of 15 m becomes 17 cm and 10 cm. Below a millimetre or so, detail stops being manufacturable and starts being suggested instead.

Drawings hit the same floor. A line half a millimetre wide represents 1.25 m of ground at 1:2,500, so a kerb, a fence and a path edge all collapse into the same mark and have to be distinguished by line style rather than by width. Deciding what will still be visible is part of choosing the scale, not something to discover after the drawing is finished.

Only lengths divide by the scale factor. Area divides by its square, so a site of one square kilometre drawn at 1:2,500 occupies 40 cm by 40 cm, which is 1,600 cm² rather than anything resembling a scaled-down million square metres. Volume, and with it mass in the same material, divides by the cube.

That cube is what makes scale models feel wrong in the hand. A solid model at 1:87 has about one six-hundred-thousandth of the volume of the original and would weigh proportionally less if it were made of the same stuff, which no model is. It is also why scaled structures cannot be tested by shrinking them — the strength of a beam falls with the square of its dimensions while the load it carries falls with the cube.

A route is the case where a single ratio cannot work. A road or a pipeline several kilometres long rises and falls by a few tens of metres, and drawn at one scale the vertical variation disappears into the thickness of the line — at 1:2,500 a thirty-metre climb is 1.2 cm spread across forty centimetres of sheet, which reads as flat.

The convention is to exaggerate the vertical, drawing the length at one ratio and the height at another perhaps ten times larger, and to state both on the drawing. The resulting profile shows every gradient clearly and misrepresents every slope, which is acceptable precisely because the two scales are declared. A profile whose vertical exaggeration is not stated is a drawing that cannot be interpreted at all.

A drawing is a conversion somebody else will have to undo, and it has to carry enough information to be undone. The ratio belongs in the title block, and a graphic scale bar belongs beside it, because the bar survives copying, resizing and printing to fit while the printed ratio does not. Anything issued as a file should also state the sheet size it was drawn for.

Then say whether measuring off is permitted at all. The conventional instruction not to scale from the drawing exists because the written dimensions are reliable and the geometry on the paper may not be, and it is the right default for anything that will be built. Where a drawing is meant to be measured — a site plan, a survey extract — it should say so and carry the bar that makes it possible.