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FreeToolsPoint — All Free Online Tools
Four calculators on one page

Math Calculators

Find what percentage one number is of a total, take a square root, convert kilometres to miles, and measure the area of a square, rectangle, circle or triangle.

Percentage Calculator

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Shows what share one number is of a total. Formula: value ÷ total × 100, rounded to two decimals. Example: 37 and 80 give Result: 46.25%. A total of zero is rejected, because nothing can be divided by zero.

Square Root Calculator

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Returns the principal, non-negative root. Formula: √n, printed to six decimals. Example: 90 gives Square Root: 9.486833, since 9.486833 × 9.486833 is just under 90. Negative numbers are rejected.

KM to Miles Converter

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Converts a distance to statute miles. Formula: kilometres × 0.621371, printed to six decimals. Example: a marathon of 42.195 km gives 42.195 KM = 26.218749 Miles. Negative distances are rejected.

Fraction Calculator

Add, subtract, multiply or divide two fractions and get an exact simplified answer, a decimal, and the arithmetic written out.

Open Fraction Calculator

Percentage Change Calculator

Compare a starting amount with a later amount and read the rise or fall as a percentage, with the reversal and compounding traps explained.

Open Percentage Change Calculator

Area Calculator

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Formulas: square side²; rectangle length × width; circle π × radius²; triangle ½ × base × height. All printed to four decimals. Example: a rectangle 3.5 by 2.4 gives Area: 8.4000 unit². Every dimension must be greater than zero.

What these four tools do

Each box above is a separate one-step calculation, meant for the moments when reaching for a spreadsheet is more work than the sum is worth: checking a test score as a percentage, sanity-checking a root in homework, reading a road sign in the other unit, or pricing floor covering for a room.

Everything is computed by JavaScript on your own device when you press the button, and the numbers you type are not sent anywhere. The two cards without input fields are links to fuller tools on their own pages, not calculators that run here.

Accepted inputs and rounding

Blank fields and text that is not a number are refused with a message naming the field. Each calculator rounds its answer for display only; nothing is rounded before the arithmetic.

CalculatorAcceptedRefusedDecimals shown
PercentageAny finite numbers, negatives includedA total of zero2
Square rootZero or aboveNegative numbers6
Kilometres to milesZero or aboveNegative distances6
AreaEach dimension above zeroZero and negative dimensions4
Editing any field clears the answer below it, so a result on screen always belongs to the numbers currently in the boxes.

Edge cases

A share above 100%

Entering 120 and 80 returns Result: 150.00%. That is correct arithmetic, not an error: 120 really is one and a half times 80. A percentage is only capped at 100 when the value is genuinely part of the total.

A root smaller than its own number

The square root of 0.25 is 0.500000. For any number between 0 and 1 the root is larger than the number, and for numbers above 1 it is smaller. Only 0 and 1 are their own square roots.

A result too large to show

Numbers can be typed in exponent form, such as 1e200. Squaring that in the area calculator overflows what JavaScript can represent, so instead of printing an infinity the tool answers Result is too large. Please use smaller values.

Common mistakes

  • Swapping the value and the total. 37 out of 80 is 46.25%; 80 out of 37 is 216.22%. The total always goes in the second field.
  • Mixing units in the area calculator. Entering a length in metres and a width in centimetres gives a number that means nothing. Convert first, then calculate.
  • Reading the area result as a specific unit. The tool prints unit² because it has no idea what you measured; if you entered feet, the answer is square feet.
  • Treating the six displayed decimals of a distance conversion as survey-grade accuracy. They come from a rounded factor, as described below.

Limits

The distance converter multiplies by 0.621371. The exact relationship is 1 international mile = 1.609344 kilometres, which makes the true factor 0.6213711922…, so the sixth decimal starts to drift at large distances: 100 km is shown as 62.137100 miles where the exact value is 62.137119. For road, running and travel distances the difference is far below the precision of the input.

These calculators handle one step at a time. There is no expression entry, no memory, no algebra, no unit tracking and no history; results are not stored and are gone when the page reloads. For chained arithmetic, powers, logarithms or trigonometry, use the scientific calculator. The area tool covers four shapes only, and the square root tool returns the real root, so negative inputs are refused rather than answered with an imaginary number.

Questions

Why does the percentage tool accept negative numbers?

Because the division is still defined. Entering −12 and 80 returns −15.00%, which is a sensible way to express a shortfall against a target. Only a total of zero is blocked.

How exact is a square root shown to six decimals?

Most roots are irrational and never terminate, so six decimals is a truncated view of an endless number. √2 is shown as 1.414214, and squaring that printed value gives 2.000001, not 2. Keep the full displayed figure if you are going to square it again.

Can the area calculator handle a parallelogram or trapezium?

Not directly, but you can split the shape. A trapezium is a rectangle plus one or two triangles, and a parallelogram uses base × height, which is the rectangle formula with the slanted side ignored.

Why does the circle option ask for a radius rather than a diameter?

The formula π × radius² is written in terms of the radius. If you measured across the circle, halve that figure before entering it. Entering a diameter by mistake makes the area four times too large.

How do I convert miles back to kilometres here?

This converter runs one way only. Divide the miles figure by 0.621371 by hand, or multiply by 1.609344 for the exact international mile. Mass conversions have their own tool, the weight converter.