SI Base Units

Type a unit or a whole formula and see it in the seven SI base units: a kilonewton becomes 1000 N = 1000 kg·m·s⁻², and 5 kg · 9.81 m/s² becomes 49.05 N. Shows the dimension, the quantity and every step — handy for checking that a formula is dimensionally right.

UnitsDimensional analysisSI

Inputs

Input examples

Type a unit or a whole formula, the way you would on paper: kN, 5 kg · 9.81 m/s² or 230 V · 10 A. Type / for a fraction, ^ for a power and * between two units (N*m), because ms means millisecond. Terms can be added with + and − when they have the same base units. For °, °C, µ, Ω, prefixes and common units, open the keyboard (the icon in the field) and choose the units tab; or type \mu, \Omega, u or ohm. Click a unit in the tables on the right to load it.

Formula or unit

What are the SI Base Units?

The International System of Units (SI) builds every unit from just seven base units: the metre, kilogram, second, ampere, kelvin, mole and candela. All other units are products and powers of these. A newton, for example, is the force that gives 1 kg an acceleration of 1 m/s², so N = kg·m·s⁻².

Since 2019 each base unit is fixed by an exact value of a constant of nature, such as the speed of light or the Planck constant, instead of by an object like the old platinum kilogram in Paris.

Writing a unit in base units is the heart of dimensional analysis: both sides of a correct equation must have the same base units. If they do not, the equation is wrong.

J= N·m = kg·m²·s⁻²

W= J/s = kg·m²·s⁻³

V= W/A = kg·m²·s⁻³·A⁻¹

rad= m/m = 1

Powers of the Base Units

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Result

Enter a unit above

The Seven Base Units

SI Brochure, Table 2

Unit	Quantity	Fixed by
s · second	time	Δν_Cs = 9 192 631 770 Hz
m · metre	length	c = 299 792 458 m/s
kg · kilogram	mass	h = 6.626 070 15 × 10⁻³⁴ J·s
A · ampere	electric current	e = 1.602 176 634 × 10⁻¹⁹ C
K · kelvin	temperature	k = 1.380 649 × 10⁻²³ J/K
mol · mole	amount of substance	N_A = 6.022 140 76 × 10²³ mol⁻¹
cd · candela	luminous intensity	K_cd = 683 lm/W

Units with Special Names

SI Brochure, Table 4

Worked Techniques

Prefixes Become Powers of Ten

Take the prefix off, write it as a power of ten, and break down what is left.

Example:

Replace Named Units One by One

Use a formula you know for the quantity (P = VI, E = Fs, F = ma) and keep substituting until only base units remain.

Example: Ω = V/A = kg·m²·s⁻³·A⁻².

Check an Equation

Both sides of a correct equation have the same base units. Terms that are added together must also match: you cannot add metres to seconds.

Example: and both give kg·m²·s⁻².

Sources & Verification

References

BIPM, The International System of Units (SI Brochure), 9th ed., 2019 — Tables 1, 2 and 4 (defining constants, base units, units with special names).
A. Thompson & B. N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 — Ch. 4 and Appendix B.