vmbo havo vwo
Scale calculator
Quick answer
Scale 1 : n means: 1 length unit on the map is n of the same units in real life.
Map → real: real = map × n. 1 : 100 and 3 cm → 300 cm.
Real → map: map = real ÷ n. Find the scale: n = real ÷ map.
Calculator
Pick the mode. cm, m or km is display only; the form does not convert between units. n and lengths must be greater than 0. A comma or a point is fine.
What is a scale?
A scale is a ratio on a map, floor plan or model: 1 : n. It is not a percentage. Percentage is part ÷ whole × 100; that lives on the percentage calculator. Here the notation stays 1 : n, with the same length unit on both sides.
In Dutch school wording, kaart means the length on the map (or drawing). A enlargement factor (“k times as large”) is the same ratio in other words: the model is k times as large as the original, or the other way round. Whole numbers on the map and in real life simplify with the gcd, the same as on the GCD and LCM calculator.
Examples by level
Dutch secondary tracks appear as badges here once: vmbo (practical), havo (middle), vwo (pre-university). The 1 : n formulas stay the same; only the examples get denser.
Classroom floor plan 1 : 50. The corridor is 4 cm on paper. How long is that corridor in real life?
- Formulareal = map × n
- Substitute4 × 50
- Real length200 cm = 2 m
Keep centimetres until you finish × n; then you may switch to meters.
Map 1 : 25 000. Two villages are 4 cm apart. How many kilometres is that?
- Formulareal = map × n
- In cm4 × 25 000 = 100 000 cm
- To km100 cm = 1 m, so 100 000 cm = 1 km
That kilometre step is unit conversion in the write-up, not a second unit in the form.
On a drawing 6 cm, in real life 150 cm. What is the scale? Then reuse the same 1 : n in a larger problem.
- Formulan = real ÷ map
- Substitute150 ÷ 6 = 25
- GCDgcd(6, 150) = 6, so 1 : 25
In a larger problem it is still the same 1 : n: first find the scale, then map × n, keep units aligned. No extra rule.
Common mistakes
Wrong
Treating scale as a percentage: 1 : 100 becomes 1%.
Right
1 : 100 is a length ratio. Percentage is a different page.
Wrong
Mixing map in cm and real in km without converting.
Right
Same unit first, then × n or ÷ n. 100 cm = 1 m, 100 000 cm = 1 km.
Wrong
On a classroom plan 1 : 50, calling a 4 cm corridor “4 × 50 = 200 m” without checking units.
Right
4 cm × 50 = 200 cm = 2 m. The factor n changes the length, not the unit.
Wrong
Entering n = 0 or a length of 0.
Right
n and lengths greater than 0. Division by 0 is not allowed.
Practice
vmbo Classroom plan 1 : 50, 4 cm on the map. How long is it in real life?
200 cm = 2 m
4 × 50 = 200 cm. Then 200 cm = 2 m.
vmbo Scale 1 : 100, 300 cm in real life. How many cm on the map?
3 cm
300 ÷ 100 = 3 cm.
havo Scale 1 : 25 000, 4 cm on the map. How many km is that?
1 km
Multiply first: 4 × 25 000 gives 100 000 cm. Then convert: 100 cm = 1 m, so 100 000 cm = 1 km.
havo 6 cm on the drawing, 150 cm in real life. What is the scale?
1 : 25
150 ÷ 6 = 25. gcd(6, 150) = 6, so 1 : 25.
vwo Why must n not be 0 when going real → map?
Division by 0 is not allowed
map = real ÷ n. Without n there is no 1 : n. A length of 0 is also not a valid scale.
In class
On vmbo, scale is often the classroom floor plan 1 : 50 or 1 : 100: corridor and room in centimetres on paper. On havo the topographic map 1 : 25 000 appears, with the step from centimetres to kilometres. On vwo the same 1 : n sits inside a larger problem: first find the scale, then convert a distance.
Map → real, real → map and finding 1 : n are in this one calculator: it is always the same ratio. An enlargement factor stays “k times as large” in the text, not an extra mode.
Next step
- How does this work? The explanation and examples are further up this page.
Learning path
- Related: Percentage calculator
Frequently asked questions
How do you go from map length to real length?
real = map × n. At 1 : 100 and 3 cm that is 300 cm.
How do you go from real length to map length?
map = real ÷ n. At 1 : 100 and 300 cm that is 3 cm. n must not be 0.
How do you find the scale 1:n?
n = real ÷ map, same unit. 6 cm and 150 cm give 1 : 25. For whole numbers, divide by the gcd.
How do you turn 1:25 000 and 4 cm into kilometres?
Multiply first: 4 × 25 000 gives 100 000 cm. Then convert: 100 cm = 1 m, so 100 000 cm = 1 km. The form has no second unit field.