Rule of 3 Calculator

Compare proportions and solve missing values with clear steps. Build accurate ratios for daily recipes. Export neat results for study, planning, pricing, and reports.

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Formula Used

The calculator uses three known values. The known quantity is a. The known result is b. The target quantity is c. The missing result is x.

Direct proportion: x = b × c ÷ a. Use this when both quantities rise or fall together.

Inverse proportion: x = a × b ÷ c. Use this when one quantity rises while the other falls.

Direct examples include price, recipe scaling, and map distance. Inverse examples include workers and time, speed and time, or shared effort.

How to Use This Calculator

  1. Select direct or inverse proportion.
  2. Enter the known quantity and its matching result.
  3. Enter the target quantity that needs a matching result.
  4. Add unit labels for clearer output.
  5. Select decimal places for rounding.
  6. Press the calculate button.
  7. Review the answer, steps, ratio checks, and exports.

Example Data Table

Type Known Quantity Known Result Target Quantity Expected Result Use Case
Direct 3 items 12 units 5 items 20 units Price or recipe scaling
Direct 8 km 40 minutes 12 km 60 minutes Same pace travel
Inverse 4 workers 10 days 8 workers 5 days Shared workload
Inverse 60 speed 4 hours 80 speed 3 hours Fixed distance timing

About the Rule of 3 Calculator

Simple Proportion Solving

The rule of 3 is a simple proportional method. It helps when three values are known and one value is missing. This calculator turns that idea into a guided tool. It can solve direct proportion problems. It can also solve inverse proportion problems. Each result includes a scale factor, a ratio view, and a clear step summary.

Direct Proportion Uses

Direct proportion is used when two quantities rise together. If three pens cost a certain amount, six pens should cost twice as much. The calculator divides the known result by the known quantity. Then it multiplies that rate by the target quantity. This is useful for prices, recipes, map distances, fuel estimates, and classroom exercises.

Inverse Proportion Uses

Inverse proportion is used when one quantity rises while the other falls. More workers may finish the same job in fewer days. Faster speed may reduce travel time. The calculator multiplies the first quantity by its result. Then it divides by the target quantity. This keeps the total work, distance, or shared load consistent.

Result Checking

The tool also helps with checking. It shows the base rate for direct problems. It shows the constant product for inverse problems. It reports the scale factor from the known quantity to the target quantity. These details make the answer easier to audit before it is copied into a report.

Rounding and Units

Rounding control is included because different tasks need different precision. Money may need two decimal places. Engineering notes may need four or more. Simple study examples may need whole numbers. You can also enter custom unit labels. That makes the result easier to read.

Exports and Review

The CSV export is useful for spreadsheets. The PDF button is useful for saving a clean record. The example table shows common patterns before you enter your own data. Use the calculator as a fast guide, but always confirm the problem type. Choosing direct or inverse proportion is the key decision.

Practical Learning

Another useful feature is comparison language. The page explains whether the target quantity is larger or smaller than the starting quantity. This helps users see the movement of the proportion, not only the final number. It supports learning, review, and quick practical decisions without hiding the math. It also reduces repeated manual checks during study sessions and planning work.

FAQs

What is the rule of 3?

The rule of 3 finds a missing fourth value when three related values are known. It works by comparing proportional relationships and solving the unknown value.

When should I use direct proportion?

Use direct proportion when both quantities move in the same direction. If one value doubles, the matching value also doubles.

When should I use inverse proportion?

Use inverse proportion when one quantity increases while the other decreases. More workers taking fewer days is a common example.

Can this calculator handle decimals?

Yes. You can enter decimal values and choose how many decimal places appear in the final result.

Why is the target quantity blocked from zero?

In inverse proportion, the target quantity is used as a divisor. A zero divisor would make the calculation invalid.

What does scale factor mean?

The scale factor shows how the target quantity compares with the known quantity. It helps explain the size of the proportional change.

What is the CSV download for?

The CSV download saves your inputs and result in a spreadsheet-friendly file. It is useful for records, reports, and later review.

Is the PDF result editable?

The PDF is mainly for saving or sharing a clean result summary. Edit the input fields first, then create a new PDF.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.