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Scale factor

Scale factor calculator

One question: by what factor did this dimension change? Enter the two measurements and you get k as an exact fraction and a decimal — the single multiplier that reproduces the change on any other dimension of the same object.

What you are scaling

Accepts 120, 4.75, 1/8 or 3' 7 1/2".

Scale by

The size the same feature should end up at. Units can differ from the start.

Derived from the unrounded factor as k² and k³.

Your answer

1.5×

Every length is multiplied by 1.5×, which is 150% of the original. 12 cm becomes 18 cm.

This is an enlargement: the result is larger than what you started with.

Before and after, to scaleOriginalScaled

Bar lengths are proportional to the calculated factor. Read the exact figures below.

Scale factor
1.5×

Exact: 3/2

Resize percentage
150%

Enter this in a print dialog or slicer

Reverse factor
0.666666…×

66.666666…% to undo it

Result
18 cm

180 mm

Equivalent ratio
1.5:1

Result : original, as a representative ratio

Difference
+6 cm

Original was 12 cm

Consequences of this factor

How length, area and volume change at this scale factor
MeasureMultiplierChange
Length (k)1.5×+50%
Area ()2.25×+125%
Volume ()3.375×+237.5%

Area and volume figures are geometric consequences of the length factor. They describe a solid, uniformly scaled shape — not hollow parts, infill, wall thickness or material behaviour.

How this was calculated

Inputs

  • Starting measurement: 12 cm = 120 mm
  • Target measurement: 18 cm = 180 mm

Formula

k = target ÷ original

k = 180 mm ÷ 120 mm

k = 1.5× = 150%

Derived effects

  • Area (k²): 2.25×
  • Volume (k³): 3.375×
  • Result size: 120 mm × k = 180 mm

Exact calculation state: 3/2 — displayed values are formatted from this fraction, never re-used after rounding.

Calculated by SnapScaleCalc from the values entered. Methodology

How this calculation works

A scale factor is a ratio, not an amount. The example above divides 18 cm by 12 cm and gets exactly 3/2 — so k = 1.5×. That number now applies to every other dimension of the same object, whatever units those were measured in: a 34 mm boss on the same part becomes 51 mm, and a 7/8" hole becomes 1 5/16".

k = target measurement ÷ original measurement

A factor of 1.5× is not the number a slicer wants

Factor notation and percentage notation describe the same change but read differently, and they are not interchangeable in conversation:

  • 1.5× multiplies. Two factors combine by multiplying them — 1.5× then 0.8× is 1.2×.
  • 150% is that same k expressed against the original, and is what a print dialog, copier or slicer expects.
  • +50% is the change alone. Applying “50%” where 1.5× was meant lands you at a third of the intended size.

Working backwards from a known factor

The factor is a multiplier, so recovering an original size is a division rather than a subtraction. Suppose the scaled part measures 180 mm and you know it was produced at 1.5×:

original = 180 ÷ 1.5 = 120 mm
check: 120 × 1.5 = 180 mm ✓

Always close the loop like that. Multiplying the recovered value back by k is a two-second check that catches the most common error on this page, which is dividing when you meant to multiply.

The reverse factor is a reciprocal

If A → B uses k, then B → A uses 1/k. Nothing else works: the reverse of 1.5× is 1 ÷ 1.5 = 2/3 ≈ 0.6667, not 0.5×, and “take off the 50% you added” lands you at 0.75× instead. The two factors multiply to exactly 1, which is what makes it a round trip.

Kept as exact fractions this identity survives any number of steps — 3/2 × 2/3 = 1 with no residue — whereas 1.5 × 0.667 = 1.0005 and the error compounds every time you do it. That is why the reciprocal is reported here as a fraction as well as a decimal, and why k below 1 is a reduction rather than a negative amount.

Why area is k² and volume is k³, briefly

Area is a product of two independent lengths and volume a product of three. Uniform scaling multiplies each of them by k, so (kL)(kW) = k²(LW) and (kL)(kW)(kH) = k³(LWH). At k = 1.5 that is 2.25× the area and 3.375× the volume. The full derivation, the consequence table and the reasons material use does not follow k³ are on why area and volume change faster than length.

The full definitions and rounding policy live on the methodology page; if percentages are the vocabulary you need, use the scale percentage calculator instead.

What this does not tell you

The factor is exact; its consequences depend on what you are scaling. The area and volume multipliers describe a solid shape scaled uniformly on every axis. They are not a material estimate for a hollow print, a shell, a frame or anything with a constant wall thickness, and they say nothing about whether the scaled object is strong enough, printable or manufacturable.

Scaling also does not scale everything: threads, fasteners, bearings, electrical clearances, minimum wall thicknesses and legal dimensions stay what they are. Where a dimension is safety-related or regulated, treat this result as arithmetic and have the design checked.

Questions people ask about this

Is a scale factor the same as a percentage?
They describe the same thing in different notations. A factor of 1.5 is 150%. The factor is easier to multiply with, the percentage is what print dialogs and slicers ask for.
What does a scale factor below 1 mean?
It is a reduction. A factor of 0.75 makes every length three quarters of its original size, which is 75%.
Why is the area multiplier not the same as the length multiplier?
Area is a product of two lengths, so it scales by the factor squared. At a factor of 2 the length doubles but the area is four times as large.
Can I mix units in the two measurements?
Yes. Enter 250 mm and 1 ft if that is what you have — both are converted to exact millimetres before the factor is calculated, so no precision is lost.