Dimensional Engine

Universal converter, dimensional analysis, and Planck scale physics.

Dimensional Analysis & Unit Engine Handbook

Mathematical Principles & Theorems

Physical quantities classified under the 7 SI base dimensions: Mass \([M]\), Length \([L]\), Time \([T]\), Electric Current \([I]\), Temperature \([\Theta]\), Amount of Substance \([N]\), Luminous Intensity \([J]\). Dimensional formula of derived quantities (e.g., Force \([M][L][T]^{-2}\), Pressure \([M][L]^{-1}[T]^{-2}\), Energy \([M][L]^2[T]^{-2}\)). Buckingham \(\pi\) theorem governs dimensional homogeneity in physical relationships. Conversion factors preserve exact dimensional equivalence across unit systems.

Operating Instructions

Select physical category: Length, Mass, Time, Speed, Acceleration, Force, Pressure, Energy, Power.
Enter numerical magnitude into the input box and select source and target units.
Click Convert to view high-precision results across SI, Imperial, and US Customary systems.
Inspect the fundamental dimensional formula breakdown and scientific notation readouts.

Controls

Select category:

From

Enter a combination of SI base units or derived units to determine the physical quantity and its dimensional MLT form.

Convert between macroscopic units and natural Planck units.

Use the right panel to explore and calculate.

Use the controls on the left to convert units across categories.

Enter an expression on the left to see its dimensional analysis.

Planck Length (lP)

1.616255 × 10⁻³⁵ m. The quantum of length.

Planck Time (tP)

5.391247 × 10⁻⁴⁴ s. Time for light to travel 1 lP.

Planck Mass (mP)

2.176434 × 10⁻⁸ kg. Mass of pointing black hole.

Planck Temp (TP)

1.416784 × 10³² K. Max meaningful temperature.