Modular Arithmetic Calculator

Need to calculate Modular Arithmetic? Use this free Modular Arithmetic Calculator in your browser. It works on phone, tablet and computer.

How to use the Modular Arithmetic Calculator

Enter a value for “Number (a)”.
Enter a value for “Modulus (n)”.
Upload your file.
Click “Calculate a mod n”.
Your result shows on the page.

Why use this Modular Arithmetic Calculator?

The Modular Arithmetic Calculator is handy for school, work and everyday decisions. It is free, easy to use and works on any device.

Try different values as often as you like
Skip manual maths and avoid simple mistakes
Get a result as soon as you enter your numbers

Modular Arithmetic Calculator – frequently asked questions

Is the Modular Arithmetic Calculator free to use?

Yes, it is free. You can use the Modular Arithmetic Calculator as often as you like without signing up.

Do I need to install anything?

No. It runs in your web browser on a phone, tablet or computer.

Is my data safe when I use the Modular Arithmetic Calculator?

The tool runs in your browser, so what you enter is processed on your own device and is not sent to our servers.

How accurate is the Modular Arithmetic Calculator?

It follows standard formulas and shows the result on the page. For important choices, such as money, health or exams, please double-check the result with an official source or a professional.

More free Calculators

Browse all Calculators on Ilmhunt, or see all free online tools.

Embed this tool on your website — free

Copy the code below to add this working tool to your own page. A small credit link stays with it — that’s all we ask.

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    &lt;title&gt;Modular Arithmetic Calculator&lt;/title&gt;
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        }
        button:hover {
            background-color: #45a049;
        }
        .result {
            margin-top: 20px;
            padding: 15px;
            background-color: #e9f5e9;
            border-radius: 4px;
        }
        #fileContent {
            white-space: pre-wrap;
            background-color: #f8f8f8;
            padding: 10px;
            border: 1px solid #ddd;
            border-radius: 4px;
            margin-top: 10px;
        }
        .error {
            color: red;
            margin-top: 10px;
        }
    &lt;/style&gt;
&lt;/head&gt;
&lt;body&gt;
    &lt;div class=&quot;calculator&quot;&gt;
        &lt;h1&gt;Modular Arithmetic Calculator&lt;/h1&gt;
        
        &lt;div class=&quot;input-group&quot;&gt;
            &lt;label for=&quot;number&quot;&gt;Number (a):&lt;/label&gt;
            &lt;input type=&quot;number&quot; id=&quot;number&quot; placeholder=&quot;Enter a number&quot;&gt;
            
            &lt;label for=&quot;modulus&quot;&gt;Modulus (n):&lt;/label&gt;
            &lt;input type=&quot;number&quot; id=&quot;modulus&quot; placeholder=&quot;Enter modulus&quot;&gt;
        &lt;/div&gt;

        &lt;button onclick=&quot;calculateModulo()&quot;&gt;Calculate a mod n&lt;/button&gt;
        &lt;button onclick=&quot;calculateModularAdditive()&quot;&gt;Calculate Additive Inverse&lt;/button&gt;
        &lt;button onclick=&quot;calculateModularMultiplicative()&quot;&gt;Calculate Multiplicative Inverse&lt;/button&gt;

        &lt;div class=&quot;result&quot; id=&quot;result&quot;&gt;&lt;/div&gt;

        &lt;hr style=&quot;margin: 20px 0;&quot;&gt;

        &lt;h2&gt;Batch Processing from File&lt;/h2&gt;
        &lt;input type=&quot;file&quot; id=&quot;fileInput&quot; accept=&quot;.txt&quot;&gt;
        &lt;button onclick=&quot;processFile()&quot;&gt;Process File&lt;/button&gt;
        &lt;div id=&quot;fileContent&quot;&gt;&lt;/div&gt;
    &lt;/div&gt;

    &lt;script&gt;
        function calculateModulo() {
            const a = parseInt(document.getElementById('number').value);
            const n = parseInt(document.getElementById('modulus').value);
            
            if (isNaN(a) || isNaN(n) || n &lt;= 0) {
                showError(&quot;Please enter valid numbers. Modulus must be positive.&quot;);
                return;
            }

            const result = ((a % n) + n) % n;
            showResult(`${a} mod ${n} = ${result}`);
        }

        function calculateModularAdditive() {
            const a = parseInt(document.getElementById('number').value);
            const n = parseInt(document.getElementById('modulus').value);
            
            if (isNaN(a) || isNaN(n) || n &lt;= 0) {
                showError(&quot;Please enter valid numbers. Modulus must be positive.&quot;);
                return;
            }

            const result = (((-a % n) + n) % n);
            showResult(`Additive inverse of ${a} mod ${n} = ${result}`);
        }

        function calculateModularMultiplicative() {
            const a = parseInt(document.getElementById('number').value);
            const n = parseInt(document.getElementById('modulus').value);
            
            if (isNaN(a) || isNaN(n) || n &lt;= 0) {
                showError(&quot;Please enter valid numbers. Modulus must be positive.&quot;);
                return;
            }

            const result = modInverse(a, n);
            if (result === null) {
                showError(`Multiplicative inverse doesn't exist for ${a} mod ${n}`);
            } else {
                showResult(`Multiplicative inverse of ${a} mod ${n} = ${result}`);
            }
        }

        function modInverse(a, n) {
            a = ((a % n) + n) % n;
            for (let x = 1; x &lt; n; x++) {
                if (((a * x) % n) === 1) {
                    return x;
                }
            }
            return null;
        }

        function processFile() {
            const fileInput = document.getElementById('fileInput');
            const file = fileInput.files[0];
            
            if (!file) {
                showError(&quot;Please select a file first.&quot;);
                return;
            }

            const reader = new FileReader();
            reader.onload = function(e) {
                const text = e.target.result;
                const lines = text.split('\n');
                let output = '';

                for (let line of lines) {
                    line = line.trim();
                    if (line === '') continue;

                    const [a, n] = line.split(' ').map(Number);
                    if (isNaN(a) || isNaN(n) || n &lt;= 0) {
                        output += `Invalid input: ${line}\n`;
                        continue;
                    }

                    const modResult = ((a % n) + n) % n;
                    const addInverse = (((-a % n) + n) % n);
                    const multInverse = modInverse(a, n);

                    output += `Input: ${a} mod ${n}\n`;
                    output += `Regular modulo: ${modResult}\n`;
                    output += `Additive inverse: ${addInverse}\n`;
                    output += `Multiplicative inverse: ${multInverse === null ? &quot;doesn't exist&quot; : multInverse}\n\n`;
                }

                document.getElementById('fileContent').textContent = output;
            };
            reader.readAsText(file);
        }

        function showResult(message) {
            const resultDiv = document.getElementById('result');
            resultDiv.textContent = message;
            resultDiv.style.color = 'black';
        }

        function showError(message) {
            const resultDiv = document.getElementById('result');
            resultDiv.textContent = message;
            resultDiv.style.color = 'red';
        }
    &lt;/script&gt;
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<p><a href="https://ilmhunt.com/modular-arithmetic-calculator/" target="_blank" rel="noopener">Modular Arithmetic Calculator</a> by <a href="https://ilmhunt.com/" target="_blank" rel="noopener">IlmHunt</a> — free online tools</p>