Vector Magnitude Calculator

INPUT SUMMARY

Current calculation basis

Entered values: Horizontal component: 300 N · Vertical component: 400 N

Converted SI values: horizontal = 300 SI · vertical = 400 SI

Engineering interpretation: Using the current inputs, calculate the magnitude of a two-dimensional perpendicular vector from its components. The current result is 500 N.

ENGINEERING PRINCIPLE

A vector magnitude follows the Pythagorean relation when its components are perpendicular.

Calculate the magnitude of a two-dimensional perpendicular vector from its components.

FORMULA & VARIABLES

R = √(Rx² + Ry²)

• R = vector magnitude (N)
• Rx = horizontal component (N)
• Ry = vertical component (N)

CALCULATION STEPS

How this result is assembled

1. Convert the entered values to the SI basis required by the formula.
2. Apply R = √(Rx² + Ry²) to the converted values.
3. Report 500 N in the selected output presentation and review the stated assumptions.

FORMULA VERIFICATION

Units, scope and reference

Reference: NIST SP 811 for unit relationships; standard classical mechanics and strength-of-materials derivations for the stated scalar relation.

Internal basis: All inputs are converted to the calculator’s SI base before the formula is evaluated.

Valid conditions: Positive finite scalar input values in the current calculator model.

Limitations: The components are perpendicular. The result reports magnitude only, not direction.

ASSUMPTIONS

Use this result in context

• The components are perpendicular.
• The result reports magnitude only, not direction.

Results must be verified by a qualified engineer and checked against applicable engineering standards, material properties, loading conditions and design requirements.

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