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Ratio, Proportion & Percentage Solver

Simplify ratios, solve proportions, allocate totals, analyse percent change, and convert map scales with transparent step-by-step working designed for classrooms and collaborative study.

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Results

How it's calculated

    For teaching use only—always check classroom examples before sharing them in assessments.

    Teacher notes

    How to use this calculator effectively

    Use this page to simplify ratios, solve proportions, and convert between ratios, fractions, and percentages with visible steps.

    How it works

    The calculator cross-multiplies proportions and reduces ratios with common factors. Keep all quantities in the same unit before solving so the result represents the intended comparison.

    When to use

    Use it for recipe scaling, map or drawing scale, mixture checks, classroom proportion problems, and quick percentage conversions.

    Common mistakes to avoid

    Interpretation and worked example

    For 3:5 = x:20, the tool cross-multiplies 5x = 60 and solves x = 12. If the answer direction feels wrong, check which side represents the same category.

    See also

    FAQ

    Which modes are included in this solver?

    The solver covers nine workflows: ratio simplification (with equivalent ratio generation), a:b=c:d proportions, part–whole–percent conversions, direct and inverse proportion, ratio splitting with optional integer rounding, percent change and reverse percent, percent comparisons highlighting percentage points versus relative change, and map scale conversions.

    How do teacher mode and sharing tools help classroom work?

    Teacher mode keeps the worked steps visible for projection or screenshots, LaTeX export supports formal notes, and the share button copies a URL with all inputs so students can revisit exactly the same example.

    What should I enter first?

    Start with the minimum required inputs shown above the calculate button, then keep optional settings at their defaults for a first run. After you get a baseline result, change one parameter at a time so you can see exactly what caused the output to move.

    How precise are the results?

    The calculator keeps internal precision and rounds only for display. Small differences can still appear when another tool uses different constants, unit assumptions, or rounding rules. Match the same assumptions before comparing values.

    Why can my result differ from another calculator?

    Different tools often choose different conventions, default rates, or date-count methods. Check units, period settings, and any hidden defaults first. If your setup matches and values still differ, use the worked example and steps section to identify the branch where methods diverge.