Calculator
Use two values for pair operations, or enter a comma separated list for list analysis.
Example data table
| Operation | Inputs | Formula | Output |
|---|---|---|---|
| Add two numbers | -8 and 3 | -8 + 3 | -5 |
| Multiply two numbers | -6 and -4 | (-6) × (-4) | 24 |
| Distance | -7 and 5 | |-7 - 5| | 12 |
| Count negatives | -8, -3, -1, 0, 4, 9 | Count x < 0 | 3 |
| List summary | -8, -3, -1, 0, 4, 9 | Count, sum, mean, median | Count 6, sum 1, mean 0.1667 |
Formula used
- a + b for signed addition.
- a - b = a + (-b) for subtraction.
- a × b for multiplication.
- a ÷ b for division, where b ≠ 0.
- a^b for powers.
- |a| for absolute value.
- |a - b| for distance on the number line.
- (a + b) ÷ 2 for average.
- Σx for list sum and Πx for list product.
- mean = Σx ÷ n and median from sorted values.
Negative number rules matter. Same signs add directly. Different signs subtract absolute values. For multiplication and division, same signs produce positives, while different signs produce negatives.
How to use this calculator
- Enter values in Number A and Number B for pair based calculations.
- Enter a comma separated list when using list operations.
- Choose the operation that matches your negative number task.
- Press Submit to display the result above the form.
- Use the CSV or PDF buttons to download the current result.
Frequently asked questions
1. What is a negative number?
A negative number is any value less than zero. It appears to the left of zero on the number line and often represents loss, debt, decrease, or direction below a reference point.
2. Why does multiplying two negatives give a positive?
The sign rule preserves consistent arithmetic patterns. Repeated subtraction and distributive reasoning show that a negative multiplied by a negative must reverse direction twice, producing a positive result.
3. How does subtraction with negatives work?
Convert subtraction into addition of the opposite value. For example, 5 - (-3) becomes 5 + 3, and -2 - 4 becomes -2 + (-4).
4. What does absolute value mean?
Absolute value is the distance from zero, so it never stays negative. For example, |-9| = 9 because nine units from zero is still a positive distance.
5. Can I use decimal negatives here?
Yes. The calculator accepts integers and decimals for pair operations and list analysis. Only the negative base power option restricts non-integer exponents because those values leave the real number system.
6. What happens if I divide by zero?
Division by zero is undefined, so the calculator stops and shows an input error. Enter any nonzero divisor to compute a valid signed quotient.
7. Why count negatives in a list?
Counting negatives helps analyze data balance, loss events, temperature drops, elevation changes, and signed datasets. It is useful when you need quick distribution insight before deeper statistical review.
8. What can the downloads be used for?
CSV downloads work well for spreadsheets and datasets. PDF downloads are useful for reports, class notes, or sharing a fixed record of the current negative number calculation.