SCALE FACTOR CALCULATOR
FIND k • APPLY k • ENLARGE • REDUCE • WORK BACKWARDS
ENLARGEMENT / REDUCTION
NEXT shows the answer. The full working is on Screen 3.
SCALE FACTOR ANSWER
RESULT • MODE • ENLARGEMENT OR REDUCTION
FULL WORKING
FORMULA • SUBSTITUTION • RESULT
Use PREVIOUS to return to the answer screen.
SCALE FACTOR FORMULAS
FIND k AND APPLY k
Find scale factor: k = new length ÷ original length.
Find new length: new = original × k.
Find original: original = new ÷ k.
Compare matching lengths from similar shapes.
ENLARGE OR REDUCE
UNDERSTAND THE VALUE OF k
If k > 1: the new length is larger.
If 0 < k < 1: the new length is smaller.
If k = 1: the length has not changed.
Example: k = 2.4 means 2.4 times as large.
WHAT THIS TOOL DOES
ENLARGEMENT • REDUCTION • SIMILAR SHAPES
This calculator helps with enlargement and reduction questions.
It can find the multiplier between two matching lengths.
It can apply a known multiplier to find a new length.
It can also work backwards to find the original length.
HOW TO USE
CHOOSE MODE • ENTER VALUES • SOLVE
Choose FIND SCALE FACTOR to calculate k from two lengths.
Choose APPLY: FIND NEW to enlarge or reduce a length.
Choose APPLY: FIND ORIGINAL to work backwards.
Press SOLVE or Enter to calculate.
WORKED EXAMPLES
FIND k AND APPLY k
Find k: original = 5, new = 12.
k = 12 ÷ 5 = 2.4, so this is an enlargement.
Find new: original = 18, k = 0.5.
new = 18 × 0.5 = 9, so this is a reduction.
WORK BACKWARDS
FIND ORIGINAL LENGTH
If the scaled length is known, divide by the scale factor.
Example: new = 15 and k = 3.
original = 15 ÷ 3 = 5.
This is useful when the original shape is missing.
COMMON SEARCHES
SEARCH INTENT COVERAGE
scale factor calculator
find scale factor from two lengths
enlargement calculator GCSE
reduction scale factor calculator
similar shapes scale factor calculator
MORE SEARCHES
READABLE SEO PAGE
apply scale factor to length
work backwards scale factor
new length calculator
original length calculator
scale drawing calculator • map scale calculator
WHO USES IT
STUDENTS • TEACHERS • DESIGNERS
Students use it for enlargement, reduction and similar shapes.
Teachers and tutors use it to demonstrate k = new ÷ original.
Designers and makers use it to resize drawings and objects.
Parents can use it to check GCSE homework answers.
COMMON USE CASES
SHAPES • DRAWINGS • PLANS
Use it for similar shapes and enlargement questions.
Use it for reductions, scale drawings and map-style problems.
Use it to resize plans, diagrams, models and measurements.
Always compare corresponding sides or matching features.
RELATED TOOLS
GEOMETRY AND RATIO LINKS
Scale factor connects with geometry, ratio and proportional reasoning.
FAQ + SEARCH TERMS
READABLE FINAL SEO PAGE
What is a scale factor? The multiplier from original to new.
What if k is greater than 1? It is an enlargement.
What if k is below 1? It is a reduction.
scale factor calculator • enlargement calculator • reduction calculator
GCSE scale factor help • similar shapes calculator