Complex Number Calculator
Add, subtract, multiply or divide two complex numbers.
Open toolQuaternion Calculator
Add or multiply quaternions, or find A’s conjugate, inverse or norm. Provide Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation to compute results directly in your browser. Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm.
Free to useNo sign-upRuns in your browser
Enter your details
Enter the inputs, then select Calculate.
Your result
Enter your details
Result will appear here
How the Quaternion Calculator Works & Core Formula
The Quaternion Calculator evaluates Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Add or multiply quaternions, or find A’s conjugate, inverse or norm.
Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm.
Quaternion Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Quaternion Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Quaternion A: w,x,y,z | 1,2,3,4 | Enter exactly four finite components in scalar-first order w, x, y, z; each within ±1e12. | Required workspace parameter |
| Input: Quaternion B: w,x,y,z | 2,1,0,1 | Enter exactly four finite components w, x, y, z for addition or multiplication; each within ±1e12. Ignored for conjugate, inverse and norm. | Required workspace parameter |
| Input: Operation | Multiplication | Options: Multiplication, Addition, Conjugate, Inverse | Required workspace parameter |
| Worked Case 1: Baseline run (Quaternion A: w,x,y,z = 1,2,3,4) | Preloaded / test values | Add or multiply quaternions, or find A’s conjugate, inverse or norm | Quaternion A: w,x,y,z = 1,2,3,4; Quaternion B: w,x,y,z = 2,1,0,1; Operation = Multiplication. Output: Quaternion (w, x, y, z): -4, 8, 8, 6; Operation: Multiplication. |
| Worked Case 2: Comparison scenario (quaternion calculator online) | Preloaded / test values | Add or multiply quaternions, or find A’s conjugate, inverse or norm | Quaternion A: w,x,y,z = 1,0,0,0; Quaternion B: w,x,y,z = 2,1,0,1; Operation = Inverse. Output: Quaternion (w, x, y, z): 1, 0, 0, 0; Operation: Inverse. |
Step-by-Step Guide to Using the Quaternion Calculator
Follow these three steps to configure Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation, verify unit and boundary rules, and export your Quaternion Calculator output.
Enter the inputs
Start with quaternion a: w,x,y,z. Enter exactly four finite components in scalar-first order w, x, y, z; each within ±1e12.
Input and settings
Check units and mode
Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm.
Tool result
Calculate and save
Select Calculate, check the labelled result, then use Copy result or Download result.txt.
Review the details
Practical Worked Examples for Quaternion Calculator
These concrete scenarios illustrate how the Quaternion Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Quaternion A: w,x,y,z = 1,2,3,4)
Quaternion A: w,x,y,z = 1,2,3,4; Quaternion B: w,x,y,z = 2,1,0,1; Operation = Multiplication. Output: Quaternion (w, x, y, z): -4, 8, 8, 6; Operation: Multiplication.
Comparison scenario (quaternion calculator online)
Quaternion A: w,x,y,z = 1,0,0,0; Quaternion B: w,x,y,z = 2,1,0,1; Operation = Inverse. Output: Quaternion (w, x, y, z): 1, 0, 0, 0; Operation: Inverse.
Boundary & unit check (Quaternion Calculator)
When solving for 'quaternion calculator', verify that Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation use consistent units and stay within the documented scope: Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm.
How to Read and Verify the Quaternion Calculator Output
The output panel reports the exact result derived from Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation alongside any unit or formatting notes.
Every calculation follows the rule: Add or multiply quaternions, or find A’s conjugate, inverse or norm. Because JavaScript uses IEEE 754 double-precision floating-point arithmetic, numeric outputs display up to 12 significant digits where applicable.
Always cross-check the displayed result against the scope note (Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm) before applying the value to production specifications, financial models, or lab records.
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Quaternion Calculator output.
Operational scope: Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
Need an adjacent calculation in Everyday Math? Use the related tools linked below to chain your workflow without leaving your browser.
More free tools to try
Choose another tool for your next calculation, conversion, or text task.
Race Fueling Calculator
Calculate carbohydrate total and an interval schedule from a supplied existing plan.
Open tool
Race Time Predictor
Extrapolate race time using a supplied distance exponent.
Open tool
ACOS Calculator
Find attributed advertising cost of sales and its difference from a supplied target.
Open tool
Alcohol Dilution Calculator
Calculate how much water to add and total final volume when diluting spirits or alcohol from initial ABV to target ABV.
Open toolFrequently Asked Questions About Quaternion Calculator
Answers about using Quaternion Calculator and understanding its results.
What formula or rule does the Quaternion Calculator use?
The Quaternion Calculator applies the rule: Add or multiply quaternions, or find A’s conjugate, inverse or norm. Enter Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Quaternion Calculator?
Yes. Provide Quaternion A: w,x,y,z, Quaternion B: w,x,y,z, Operation using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Quaternion Calculator?
Components are scalar-first (w,x,y,z); multiplication is the Hamilton product A×B and is order-dependent. Conjugate, inverse and norm use A only. The zero quaternion has no inverse; no implicit rotation normalization occurs. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Quaternion B is ignored for conjugate, inverse and norm. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Quaternion Calculator free and does it keep my inputs private?
Yes. All calculations for the Quaternion Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
Try your own values
Choose another tool for your next calculation, conversion, or text task.