Long Division Calculator
Calculated using standard mathematical and industry formulas.
Free online Long Division Calculator calculator and unit conversion tool for everyday, engineering, and home projects.
How to use this calculator?
- Enter the dividend (the number being divided) and the divisor.
- Read the integer quotient Q, remainder R, mixed number, and exact decimal.
- Use the verification formula D = (d × Q) + R to confirm the result.
Formula & calculation method
Integer division algorithm
Q = ⌊D / d⌋ · R = D − (d × Q) · Verification: D = (d × Q) + R
D = dividend, d = divisor, Q = quotient, R = remainder.
Step-by-step calculation example
487 ÷ 12: Q = ⌊487/12⌋ = 40, R = 487 − (12 × 40) = 7. Verification: 12 × 40 + 7 = 487 ✓
Key insights to remember
- Long division is the basis of polynomial division, Euclidean GCF algorithm, and modular arithmetic.
- The remainder R is always 0 ≤ R < divisor. If R = 0, the dividend is exactly divisible.
- Modular arithmetic uses the remainder: 487 mod 12 = 7 (remainder from this example).
- The decimal result D / d can be expressed as the mixed number Q R/d for non-zero remainders.
How to interpret your results?
Quotient and remainder
D = d × Q + R. The quotient Q is the number of complete groups; R is what is left over.
Mixed number
Q R/d expresses the result as a whole part plus a proper fraction. 487 ÷ 12 = 40 remainder 7 → 40 7/12.
Frequently asked questions
- How do I use the Long Division Calculator calculator?
- Enter your numerical input and select desired units to get instant accurate results.
- How accurate are the conversions?
- Conversions use official ISO conversion factors for maximum precision.
- Does it convert metric and imperial units?
- Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.
- Is my data stored?
- No, all calculations execute 100% locally in your browser with zero data logging.
- Can I use this for DIY or engineering projects?
- Yes, it provides reliable estimates for construction, crafting, science, and everyday math.
- What if I enter invalid inputs?
- The calculator will display a friendly error prompt if non-numeric values are entered.
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