Units and quantities

In Physics mode, numbers carry units. Quantus checks that they fit, converts between them and names the result.

Calculate with units

Write the unit straight after the number:

\frac{1}{2} \cdot 3kg \cdot (4\frac{m}{s})^2

SYMBOLIC	$\frac{1}{2} \cdot 3\,\mathrm{kg} \cdot (4\,\frac{\mathrm{m}}{\mathrm{s}})^{2}$
STEP	$24\,\frac{\mathrm{kg} \cdot \mathrm{m}^{2}}{\mathrm{s}^{2}}$
RESULT	$24\,\mathrm{J}$

Next to the result Quantus shows the name of the quantity (energy) and its dimension.

Units are converted to a common one

3km + 200m

SYMBOLIC	$3\,\mathrm{km} + 200\,\mathrm{m}$
STEP	$3\,\mathrm{km} + 0{,}2\,\mathrm{km}$
RESULT	$3{,}2\,\mathrm{km}$

The first unit sets the target. Units you typed yourself are kept: 72\frac{km}{h} stays in $\mathrm{km/h}$. Only a product the arithmetic made, such as $\mathrm{kg \cdot m^2/s^2}$, is replaced by its named unit.

note

There is no command to convert into a unit of your choice yet. Divide by that unit instead: \frac{72\,\mathrm{km/h}}{1\,\mathrm{m/s}} gives $20$.

Work with variables

Define the quantities once with an indexed name, then use them:

U_1 = 230V
R_1 = 4{,}7k\Omega
P = U_1 \cdot \frac{U_1}{R_1}

SYMBOLIC	$P = U_{1} \cdot \frac{U_{1}}{R_{1}}$
SUBSTITUTED	$P = 230\,\mathrm{V} \cdot \frac{230\,\mathrm{V}}{4{,}7\,\mathrm{k\Omega}}$
STEP	$P = 11255{,}319\ldots\,\frac{\mathrm{V}^{2}}{\mathrm{k\Omega}}$
RESULT	$P = 11{,}255319\ldots\,\mathrm{W}$

Lower Settings → Precision if 50 digits are more than you need.

Physical constants

The CODATA constants have reserved names, such as c_0, g_n, k_B or \hbar:

E = m_e \cdot c_0^2

$$E = 8{,}18710577682388596779369446 \cdot 10^{-14}\,\mathrm{J}$$

The full list is in Units and constants.

Dimension errors

Quantus refuses what does not fit physically, and says why:

Input	Message
3m + 2s	Incompatible units: m (length) and s (time) cannot be added.
2^{3m}	The exponent must be dimensionless but carries the unit m (length).
25°C + 1K	℃ (temperature) and K (temperature) cannot be added directly because one of them has a zero point of its own.

Angles

30^\circ is in degrees, everything else in radians: \sin(30^\circ) \cdot 10N gives $5\,\mathrm{N}$.

See also

• Units and constants
• Concepts: why letters become units