🔬 Technical Specification

Metrology Methodology & Formulas

Comprehensive documentation of all conversion factors, SI base definitions, floating-point rounding algorithms, and automated test validations.

Author / Metrology Reviewer: WeightMaster Technical Team
Standard Basis: BIPM SI Brochure (9th Edition) & NIST SP 811
Last Reviewed: October 2026
Test Verification: 100% Round-trip Precision Within 1e-9

1. The Two-Step Canonical Base-Unit Algorithm

To avoid combinatorial multiplication errors across $N \times (N-1)$ unit pairs, WeightMaster uses the standard metrological Base-Unit Model anchored to the SI Kilogram ($\text{kg}$):

$$\text{Value}_{\text{kg}} = \text{Input} \times \text{Factor}_{\text{from}}$$ $$\text{Output} = \frac{\text{Value}_{\text{kg}}}{\text{Factor}_{\text{to}}}$$

Every unit factor represents the exact legal or physical quantity of kilograms contained within one unit.

2. Complete Master Table of Conversion Factors

The table below lists all constants used in our calculation engine. Every factor is an exact defined integer or finite decimal fraction in metrological law:

Unit Name Symbol Category Exact Kilograms per Unit (kg) Governing Standard
Kilogram kg SI Base 1 (Exact Base) BIPM SI Definition (2019)
Gram g SI Metric 0.001 $10^{-3}\text{ kg}$
Milligram mg SI Metric 0.000001 $10^{-6}\text{ kg}$
Microgram µg SI Metric 0.000000001 $10^{-9}\text{ kg}$
Metric Tonne t SI Metric 1000 $10^{3}\text{ kg}$
Pound (Avoirdupois) lb / lbs Imperial / US 0.45359237 1959 International Agreement
Ounce (Avoirdupois) oz Imperial / US 0.028349523125 $0.45359237 \div 16\text{ kg}$
Stone st British Customary 6.35029318 $0.45359237 \times 14\text{ kg}$
Short Ton (US) ton (US) US Customary 907.18474 $0.45359237 \times 2000\text{ kg}$
Long Ton (UK) ton (UK) Imperial 1016.0469088 $0.45359237 \times 2240\text{ kg}$
Troy Ounce ozt Precious Metals 0.0311034768 LBMA & UK Weights Act 1878
Carat (Metric) ct Gemstones 0.0002 CGPM 1907 (200 mg exact)
Tola tola South Asian Bullion 0.0116638038 180 Troy Grains (India/Pakistan)
Grain gr Historic / Ballistic 0.00006479891 $0.45359237 \div 7000\text{ kg}$
Slug slug Aerospace Physics 14.593903 $1\text{ lbf} \cdot \text{s}^2/\text{ft}$
Atomic Mass Unit u / amu Nuclear Physics 1.66053906660e-27 CODATA 2018 Constant

3. Floating-Point Arithmetic & Rounding Control

Standard IEEE 754 binary floating-point computation can produce trailing rounding artifacts (such as 0.1 + 0.2 = 0.30000000000000004). To maintain clean and reliable display:

  • •
    Precision Settings: Users can select 0, 2, 4, or 6 decimal places, or Auto. In Auto mode, trailing zeros are cleanly stripped while retaining up to 6 significant digits.
  • •
    Scientific Notation: Values smaller than $1 \times 10^{-6}$ or larger than $1 \times 10^{9}$ automatically switch to standard scientific E-notation (e.g. $1.6605\text{e-27}$) to prevent unwieldy digit overflows.

4. Automated Unit Verification & Round-Trip Tests

Our calculation algorithms are verified continuously against standard test fixtures: