About this tool
The modulo operation returns the remainder of integer division. It's fundamental to clock arithmetic (24-hour wraparound), checksums (credit card, ISBN), hash tables, and cryptography (RSA, ECC). Programming languages differ on how they handle negative numbers, but mathematicians always want the result in [0, n).
How it works
Enter dividend and divisor. The calculator returns the remainder using the mathematical convention (always non-negative when n is positive).
How to use the Modulo Calculator
The Modulo Calculator is a browser-based tool that runs entirely on your device. Inputs you enter never reach a server - all calculations happen client-side in JavaScript. This means:
- Privacy: nothing is logged, sent, or stored by 3Tej. Inputs disappear when you close the tab.
- Speed: results update as you type. No network round trip.
- Offline use: once the page is cached, it works without internet.
- No signup: no account, no email, no rate limits.
Step by step
- Enter your inputs in the form above. Each field is labeled with its unit (currency, percent, kg, etc.) and the expected range.
- Read the result as it updates. The number reflects the formula commonly accepted in Modulo-related calculations.
- Adjust to see sensitivity: change one input at a time and watch how the output moves. This is the fastest way to understand which variable matters most.
- Copy or screenshot the result for later reference. The page state persists for the session if your browser allows it.
When you would use this
- Quick estimates: when you need a number now and don't want to open a spreadsheet.
- Sensitivity analysis: testing how a result changes as inputs vary, before committing to a real-world decision.
- Comparison: running the same calculation with different inputs to compare options side by side.
- Learning: building intuition for how the underlying math behaves.
- Documentation: capturing a snapshot of inputs and outputs at a point in time.
The formula explained
This calculator uses the following formula:
a mod n = a - floor(a / n) · n; result is always in [0, n) for positive n
The reason this formula works is rooted in the underlying physics, finance, or biology of the problem. Behind every calculator is a published, peer-reviewed equation or a widely accepted convention. We do not invent formulas; we apply standard ones from textbooks, government tables, professional bodies, and academic literature.
If you are curious about the math, the simplest way to verify is to plug in two known numbers and compare against a known result. The calculator should match published examples to within rounding precision.
Frequently asked questions
Why does a mod n = a for a < n?
Integer division gives 0, so a - 0·n = a. 3 mod 5 = 3 because 5 doesn't go into 3 even once.
Negative dividend?
Mathematicians: -7 mod 3 = 2 (always non-negative). C/JavaScript %: -7 % 3 = -1 (matches sign of dividend). Python: %: matches divisor. We use the math convention.
Real-world use?
Hour wrap (25 mod 24 = 1), even/odd test (n mod 2), RSA encryption, ISBN-10 check digit, day-of-week calculation.
a mod 0?
Undefined - division by zero. The calculator returns an error.
Is the Modulo Calculator accurate?
The Modulo Calculator applies the standard formula for modulo. Accuracy is limited only by your input precision. For decisions with material consequences, use the result as a starting point and verify with a qualified professional or the relevant official source.
Is the Modulo Calculator free?
Yes. 100% free, no signup, no payment, no API key. The site is funded by display ads that appear around the tool but not inside the calculation flow.
Are my inputs saved?
No. Inputs stay in your browser tab. Closing the tab discards them. The site uses Google Analytics for traffic measurement (anonymized) but does not see what you type into the form.
Can I use the Modulo Calculator on my phone?
Yes. The tool is responsive and tested on iOS Safari, Android Chrome, and major desktop browsers. Touch targets meet Apple's 44pt and Google's 48dp minimum guidance.
How do I report a bug or suggest improvement to the Modulo Calculator?
Email hi@3tej.com with the URL of this page and a description of what you saw vs expected. We typically respond within 72 hours and update calculators when rules or formulas change.
How accurate is the Modulo Calculator?
It applies the standard formula. Accuracy is limited only by your input precision. For decisions with material consequences (taxes, medical, legal, structural), use the result as a starting point and verify with a qualified professional in the relevant field.
Is the Modulo Calculator free to use?
Yes. 100% free, no signup, no payment, no API key. The site is funded by display ads around the tool but not inside the calculation flow.
Are my inputs saved anywhere?
No. All inputs stay in your browser tab. Closing the tab discards them. The site uses Google Analytics for traffic measurement (anonymized) but the analytics never see what you type into the form.
Does the Modulo Calculator work offline?
Yes. Once the page has loaded, it works without internet. The calculation runs in JavaScript on your device.
Can I share results from the Modulo Calculator?
Take a screenshot or copy the output. The page doesn't generate shareable URLs for specific calculations - inputs stay in your browser only.
Why are the results different from another modulo tool?
Most likely: different formula assumptions, different default values, different rounding rules, or different applicable rates. Check the methodology if both tools document it. Both can be valid for different scenarios.