CALCULATE WITH CONFIDENCE

Algebra & Equations

Quaternion Calculator

Calculate quaternion with validated inputs and explicit results.

Algebra & Equations

Enter values

Private calculation in your browser

Use the notation shown in each label and example. Inputs stay on this device and are never sent to a calculation service.

Result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Enter values using the notation shown beside each field.
  2. Choose a calculation mode when the tool offers more than one interpretation.
  3. Read the primary answer first, then inspect the supporting details.

Calculation method

Apply the stated definition

Use Hamilton's quaternion multiplication rules.

The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.

Worked example

Worked example

Enter the example values shown in the fields to verify the stated relationship.

Use Hamilton's quaternion multiplication rules.

Supported inputs

Precision and limits

Finite, bounded input

Numeric inputs use finite JavaScript floating-point values with magnitude limits. Results are normally displayed to 12 significant digits; outputs labelled approximate are not exact identities.

Notation

Enter ordinary finite decimals. Polynomial fields use coefficients in descending powers, separated by commas; for example 1, −3, 2 means x² − 3x + 2.