Choose a comparison mode
Expressions are evaluated safely without PHP eval(). Supported examples include 2/3, 2 1/3, 125%, sqrt(81), abs(-7), 2^10, and 3e-4.
Formula used
Basic comparison
The calculator evaluates both inputs first. It then compares their numeric values using the selected equality tolerance.
Differences
Absolute difference = |A − B|
A positive signed difference means A is greater. A negative signed difference means A is smaller.
Percentage difference
Symmetric difference = 2|A − B| ÷ (|A| + |B|) × 100
The relative formula uses B as its reference. The symmetric formula treats both values equally.
Range test
Inclusive boundaries use ≤. Exclusive boundaries use < and do not include equal endpoint values.
How to use this calculator
- Select a mode for two values, multiple values, a range, measurements, dates, or a linear inequality.
- Enter numbers directly or use supported expressions, fractions, percentages, powers, roots, and common functions.
- Choose the relation, ordering, units, boundaries, timezone, precision, or tolerance needed for your comparison.
- Select Compare values. The result appears above the form with details, steps, and visual explanations.
- Copy, print, save to local history, or export saved comparisons as a CSV file.
Greater-than and less-than symbol guide
7 > 4
3 < 8
5 = 5
9 ≥ 9
2 ≤ 6
4 ≠ 10
A useful memory aid is that the wide, open side faces the larger number. The narrow point faces the smaller number.
Comparison history
Saved entries remain in this browser using local storage. No database is required.
| Date | Mode | Result | Action |
|---|---|---|---|
| No saved comparisons yet. | |||
Understanding numerical comparisons
Comparing values means deciding which quantity is larger, smaller, or equal. For positive whole numbers, the value farther right on a number line is greater. Decimal values follow the same rule, but comparing matching place values is helpful. For example, 4.50 equals 4.5 because trailing zeros do not change a decimal’s value.
Negative numbers reverse common intuition
Among negative numbers, the value closer to zero is greater. Therefore, −2 is greater than −8. A temperature of −2 degrees is warmer than −8 degrees, and a balance of −2 is less negative than a balance of −8. The number line makes this easier because −2 appears farther right.
Fractions and mixed numbers
Fractions can be compared by converting them to decimals, finding a common denominator, or cross-multiplying. For positive denominators, a/b is greater than c/d when a × d is greater than c × b. Mixed numbers should first be converted to improper fractions or evaluated as a whole number plus a fraction.
Percentages and decimals
A percentage is a number divided by one hundred. Thus, 75% equals 0.75 and 3/4. Entering different formats does not change the underlying comparison because this calculator evaluates each format numerically before applying the relation.
Floating-point tolerance
Computers store many decimal numbers approximately. Calculations such as 0.1 + 0.2 may be extremely close to 0.3 without using the identical stored binary value. Equality tolerance treats values as equal when their difference is tiny relative to their magnitude. Reduce tolerance for stricter comparisons, or increase it carefully when measured values contain known uncertainty.
Measurements need matching units
One meter and thirty-six inches cannot be compared fairly by their written numbers alone. The measurement mode converts both values to a shared base unit first. Temperature uses special conversion formulas because its scales have different zero points, while length, mass, volume, and time use multiplication factors.
Inclusive and exclusive ranges
An inclusive range contains its endpoint, such as 1 ≤ x ≤ 10. An exclusive range omits an endpoint, such as 1 < x < 10. Brackets usually indicate included endpoints, while parentheses indicate excluded endpoints. This distinction matters for age limits, score bands, validation rules, and programming conditions.
Common comparison mistakes
Do not compare fraction numerators without considering denominators. Do not assume a longer decimal is automatically larger. Remember that negative values become smaller as their absolute magnitude grows. When comparing percentages, confirm whether you need percentage points, relative percentage change, or symmetric percentage difference because these measurements answer different questions.
Frequently asked questions
Can I compare mathematical expressions?
Yes. Use arithmetic operators, parentheses, powers, percentages, fractions, mixed numbers, and supported functions such as sqrt(), abs(), min(), and max().
Why can two decimals be treated as equal?
The equality tolerance handles tiny floating-point differences. This is useful when values come from calculations rather than exact typed integers.
Can the calculator order many numbers?
Yes. The multiple-values mode sorts up to 200 entries, creates a chained inequality, identifies minimum and maximum values, and reports duplicates.
Does the inequality solver handle quadratic equations?
No. The included solver is intentionally limited to linear expressions in x. It detects nonlinear inputs and returns an explanatory error.
Where is history stored?
History is stored locally in the current browser. Clearing browser storage or using a different device will remove or hide those entries.