Greek Alphabet, SI Prefixes, Units and Drawing Symbols

November 3, 2026 · Indumor

The machinist's reference handbook · Appendix B← Previous | Next → | Print

In this chapter

The Greek letters
SI prefixes
Units
Drawing and formula symbols
Roman numerals
Constants and how numbers are written

The kilogram is the only SI base unit that carries a prefix in its name; that is why its multiples are built on the gram: mg and Mg, never µkg. This appendix is made of oddities like that: the Greek letters in the handbook's formulas, the prefixes, the symbols a drawing uses without explaining, and the rules for writing a number so that a machinist in Córdoba and a buyer in Houston read it the same way.

The Greek letters

Of the twenty-four, the shop uses about fifteen: α, β and γ are the tool angles per ISO 3002, ρ is density, σ and τ are stresses, η is efficiency and ω is angular speed. One is spoken but never written: in an Argentine shop a hole "de fi 20" is 20 mm in diameter, yet the drawing says Ø. And one is written two ways without anyone noticing: the micro sign µ (U+00B5) and the letter mu μ (U+03BC) look identical, so a search for "µm" can miss a PDF typed with the other one.

The 24 Greek letters and what they usually mean in the shop and in the formulas of this handbook
Letter	Upper	Lower	Spanish name	What it usually means
alpha	Α	α	alfa	Tool clearance angle (ISO 3002), thermal expansion coefficient, gear pressure angle (20°)
beta	Β	β	beta	Helix angle (gears, cutters, threads), wedge angle of the cutting edge
gamma	Γ	γ	gamma	Tool rake angle; specific weight
delta	Δ	δ	delta	Δ: difference or increment (ΔL, ΔT); δ: deflection of a beam, cutting angle (α + β)
epsilon	Ε	ε	épsilon	Unit strain (ε = ΔL/L); tool included angle
zeta	Ζ	ζ	dseta (zeta)	Head-loss coefficient in hydraulics; rare in the shop
eta	Η	η	eta	Efficiency (η = 0.9 is 90 %)
theta	Θ	θ	zeta (theta)	Any angle; Celsius temperature in formulas (ISO 80000)
iota	Ι	ι	iota	Not used: looks like an i
kappa	Κ	κ	kappa	Tool cutting edge angle (κr, ISO 3002)
lambda	Λ	λ	lambda	Cutting edge inclination (λs), thread lead angle, thermal conductivity, column slenderness
mu	Μ	μ	mi (mu)	Friction coefficient; the micro prefix (µm), one millionth
nu	Ν	ν	ni (nu)	Poisson's ratio (0.3 for steel); kinematic viscosity
xi	Ξ	ξ	xi	Assorted coefficients; rarely seen
omicron	Ο	ο	ómicron	Not used: looks like an o
pi	Π	π	pi	π = 3.1416, circumference divided by diameter; Π: product
rho	Ρ	ρ	ro (rho)	Density (steel 7.85 kg/dm³, chapter 22); resistivity; radius of curvature
sigma	Σ	σ	sigma	σ: normal stress (MPa), standard deviation; Σ: sum
tau	Τ	τ	tau	Shear stress, in MPa
upsilon	Υ	υ	ípsilon	Rarely used
phi	Φ	φ	fi (phi)	Friction angle, phase angle, shear angle in cutting; Argentine shops say "fi 20" for a 20 mm diameter (the drawing uses Ø); Φ: magnetic flux
chi	Χ	χ	ji (chi)	Statistics (χ²); rare in the shop
psi	Ψ	ψ	psi	Auxiliary angle; face-width factor in gears
omega	Ω	ω	omega	ω: angular speed in rad/s (ω = 2πn/60, chapter 24); Ω: ohm

SI prefixes

The shop needs six or seven: the kilo of kN and kW, the mega of MPa (exactly 1 N/mm², the fact that saves the most arithmetic), the giga of the modulus of steel (210 GPa, about 30 000 ksi), the everyday milli, the micro of surface roughness, and the deca on slings and shackles, where 1 daN is taken as 1 kgf. Case matters: k is kilo and K is kelvin, m is milli and M is mega, so 5 mN and 5 MN differ by nine zeros.

SI prefixes (BIPM, 9th edition) from yotta to yocto, with the name of the number in English and in Spanish
Prefix	Symbol	Factor	That is	In Spanish	Example
yotta	Y	10²⁴	septillion	cuatrillón	YB
zetta	Z	10²¹	sextillion	mil trillones	ZB
exa	E	10¹⁸	quintillion	trillón	EJ
peta	P	10¹⁵	quadrillion	mil billones	PB
tera	T	10¹²	trillion	billón	TB, TW
giga	G	10⁹	billion	mil millones	GPa (steel has E = 210 GPa), GB
mega	M	10⁶	million	millón	MPa, MW, MHz
kilo	k	10³	thousand	mil	kN, kW, kg, km
hecto	h	10²	hundred	cien	hPa (1013 hPa atmospheric pressure), hl
deca	da	10¹	ten	diez	daN (1 daN ≈ 1 kgf, on slings and shackles)
deci	d	10⁻¹	tenth	décimo	dm³ (the litre), dB
centi	c	10⁻²	hundredth	centésimo	cm, cl
milli	m	10⁻³	thousandth	milésimo	mm, ml, mA, ms
micro	µ	10⁻⁶	millionth	millonésimo	µm (Ra 3.2 µm), µF
nano	n	10⁻⁹	billionth	milmillonésimo	nm
pico	p	10⁻¹²	trillionth	billonésimo	pF
femto	f	10⁻¹⁵	–	–	fs
atto	a	10⁻¹⁸	–	–	as
zepto	z	10⁻²¹	–	–	–
yocto	y	10⁻²⁴	–	–	–

In 2022 the BIPM added ronna (R, 10²⁷), quetta (Q, 10³⁰), ronto (r, 10⁻²⁷) and quecto (q, 10⁻³⁰). Watch the number names: a Spanish billón is a trillion, not a billion.

Units

Seven base units and, among the derived ones, the newton, the pascal, the joule, the watt, the hertz, the degree Celsius and the radian; alongside them live the minute, the hour, the litre, the tonne and the bar, which the SI accepts or tolerates. Torque is written N·m and not J, because they are different quantities. The factors for moving between metric and inch units are in chapter 1.

SI base units, named derived units and the units accepted for use with the SI (BIPM, ISO 80000-1)
Quantity	Unit	Symbol	In other units
length	metre	m	base unit
mass	kilogram	kg	base unit (the only one with a prefix in its name)
time	second	s	base unit
electric current	ampere	A	base unit
thermodynamic temperature	kelvin	K	base unit; no degree sign
amount of substance	mol	mol	base unit
luminous intensity	candela	cd	base unit
force	newton	N	kg·m/s² (1 kgf = 9.80665 N)
pressure, stress	pascal	Pa	N/m² (1 MPa = 1 N/mm²; 1 bar = 100 kPa)
energy, work	joule	J	N·m (1 kWh = 3.6 MJ; 1 kcal = 4.1868 kJ)
power	watt	W	J/s (1 HP = 745.7 W; 1 CV = 735.5 W)
frequency	hertz	Hz	1/s
Celsius temperature	degree Celsius	°C	K − 273.15
plane angle	radian	rad	m/m (1 rad = 57.2958°)
electric charge	coulomb	C	A·s
voltage	volt	V	W/A
electrical resistance	ohm	Ω	V/A
torque (moment)	newton metro	N·m	Not written as J even though the units match
angular speed	radian per second	rad/s	ω = 2π · n / 60, with n in rpm
time (accepted)	minute, hour, day	min, h, d	60 s, 3600 s, 86 400 s
angle (accepted)	degree, minute, second	°, ′, ″	1° = π/180 rad; 1′ = 1/60°; 1″ = 1/60′
volume (accepted)	litre	L, l	dm³
mass (accepted)	tonne	t	1000 kg
pressure (outside SI, in common use)	bar	bar	100 kPa = 1.01972 kgf/cm²

Drawing and formula symbols

The diameter symbol has four look-alikes: the capital Ø with stroke (U+00D8), which goes on dimensions and is typed with Alt+0216; the lowercase ø, which appears by mistake; the Unicode sign ⌀, which few fonts draw properly; and the Greek φ, which is spoken but not written. The drawing shows each dimensioning symbol on a plate; chapter 25 has the full list.

Drawing and formula symbols, with their Unicode code point and how to type them on Windows (Alt + number on the numeric keypad)
Symbol	Unicode	Name	Note
Ø	U+00D8	diameter	On dimensions (ISO 129-1); Alt+0216 on Windows
ø	U+00F8	lowercase o with stroke	Not for dimensions: a typing slip
⌀	U+2300	diameter sign	The dedicated Unicode glyph; many fonts lack it
∅	U+2205	empty set	Looks alike, but it is a maths symbol
φ	U+03C6	phi (Greek letter)	Spoken "fi 20" means Ø20; the drawing uses Ø
R	–	radius	R10; SR is spherical radius
□	U+25A1	square	□30: a 30 mm square
SØ	–	spherical diameter	SØ40
±	U+00B1	plus-minus	Symmetrical tolerance: 50 ± 0.1; Alt+0177
∠	U+2220	angle	Angularity in GD&T; a dimension carries only the value and °
⌒	U+2312	arc	Arc length: ⌒ 85; profile of a line in GD&T
°	U+00B0	degree	30°; °C with a space before it: 20 °C; Alt+0176
′	U+2032	minute (and foot)	12°30′; 6′ is 6 feet
″	U+2033	second (and inch)	12°30′15″; 1/2″ is half an inch
‰	U+2030	per mille	Slopes: 2 ‰ is 2 mm per metre
≈	U+2248	approximately equal	π ≈ 3.14
≤ ≥	U+2264, U+2265	less than or equal, greater than or equal	Ra ≤ 1.6
∝	U+221D	proportional to	P ∝ n³ for a fan
√	U+221A	square root	√2 = 1.4142
∑	U+2211	summation	Different from the letter Σ (U+03A3), which looks the same
∞	U+221E	infinity	tan 90° = ∞
×	U+00D7	times (product, count)	4 × Ø8; 100 × 50 × 5; not the letter x; Alt+0215
·	U+00B7	middle dot	N·m, kgf·m; Alt+0183
µ	U+00B5	micro sign	µm; Alt+0181; different from the letter μ (U+03BC): a search for one may miss the other
² ³	U+00B2, U+00B3	squared, cubed	mm², m³; Alt+0178, Alt+0179
⟂ ∥	U+27C2, U+2225	perpendicular, parallel	Geometric tolerances (chapter 25)
Δ	U+0394	delta (increment)	ΔT = 50 °C; the ∆ at U+2206 is a different code point

Roman numerals

They still turn up in project phases, manual volumes and the classes of a standard. Seven symbols and two rules: add from left to right, and a smaller symbol in front of a larger one is subtracted (IV, IX, XL, XC, CD, CM). No symbol is repeated more than three times in a row, except the IIII on clock faces.

The seven Roman numeral symbols and their rules
Symbol	Value	Rule
I	1	Repeated up to three times: III
V	5	Never repeated; IV is 4
X	10	IX is 9, XL is 40
L	50	Never repeated; XC is 90
C	100	CD is 400, CM is 900
D	500	Never repeated
M	1000	MMXXVI is 2026; a bar on top multiplies by a thousand

Roman numerals 1 to 100
No.	Roman	No.	Roman	No.	Roman	No.	Roman	No.	Roman
1	I	21	XXI	41	XLI	61	LXI	81	LXXXI
2	II	22	XXII	42	XLII	62	LXII	82	LXXXII
3	III	23	XXIII	43	XLIII	63	LXIII	83	LXXXIII
4	IV	24	XXIV	44	XLIV	64	LXIV	84	LXXXIV
5	V	25	XXV	45	XLV	65	LXV	85	LXXXV
6	VI	26	XXVI	46	XLVI	66	LXVI	86	LXXXVI
7	VII	27	XXVII	47	XLVII	67	LXVII	87	LXXXVII
8	VIII	28	XXVIII	48	XLVIII	68	LXVIII	88	LXXXVIII
9	IX	29	XXIX	49	XLIX	69	LXIX	89	LXXXIX
10	X	30	XXX	50	L	70	LXX	90	XC
11	XI	31	XXXI	51	LI	71	LXXI	91	XCI
12	XII	32	XXXII	52	LII	72	LXXII	92	XCII
13	XIII	33	XXXIII	53	LIII	73	LXXIII	93	XCIII
14	XIV	34	XXXIV	54	LIV	74	LXXIV	94	XCIV
15	XV	35	XXXV	55	LV	75	LXXV	95	XCV
16	XVI	36	XXXVI	56	LVI	76	LXXVI	96	XCVI
17	XVII	37	XXXVII	57	LVII	77	LXXVII	97	XCVII
18	XVIII	38	XXXVIII	58	LVIII	78	LXXVIII	98	XCVIII
19	XIX	39	XXXIX	59	LIX	79	LXXIX	99	XCIX
20	XX	40	XL	60	LX	80	LXXX	100	C

Constants and how numbers are written

ISO 80000-1 accepts either the comma or the point as the decimal sign, ISO drawings customarily carry the comma, Argentina uses the comma and ASME drawings use the point; thousands are grouped with a thin space and never with a point or a comma, because 1.250 is twelve hundred and fifty in Córdoba and one and a quarter in Houston. A space goes between the number and the unit, also in 20 °C, and the unit symbol takes no full stop and no plural.

Constants that show up in shop arithmetic
Symbol	Value	What it is
π	3.14159265	Circumference divided by diameter
π/4	0.78539816	Circle area = π/4 · D²
1/π	0.31830989	Diameter from the perimeter: D = P/π
e	2.71828183	Base of natural logarithms
√2	1.41421356	Diagonal of a unit square; side ratio of A-series sheets
√3	1.73205081	Diagonal of a unit cube
2/√3	1.1547005	Hexagon: across corners = across flats × 1.1547
√2/2	0.70710678	sen 45° = cos 45°
√3/2	0.8660254	sin 60°; height of a unit equilateral triangle
g	9.80665 m/s²	Standard gravity, exact by convention; 1 kgf = 9.80665 N
1 rad	57.2957795°	One radian in degrees (180/π)
1°	0.01745329 rad	One degree in radians (π/180)
ln 2	0.69314718	Natural log of 2
ln 10	2.30258509	Natural log of 10
1 in	25.4 mm	Inch, exact since 1959 (chapter 1)

How numbers and units are written (ISO 80000-1, BIPM)
Rule	Right	Wrong
Decimal point in English and on ASME drawings; ISO 80000-1 and the BIPM allow either, and ISO drawings customarily use the comma	12.5 mm	12,5 mm on a US drawing
Thousands with a thin space, never a point or a comma (ISO 80000-1)	12 500 mm	12,500 mm (twelve thousand five hundred, or 12.5 in Europe?)
Four-digit numbers usually go without a separator; 1 250 is not an error, just less common (BIPM)	1250 mm	1,250 mm
Space between number and unit; the symbol takes no plural and no full stop	25 kg, 3 mm	25kg, 25 kgs, 3 mm.
Upper and lower case in the symbol matter	kN, MPa, mm, kg	KN, mpa, MM, Kg
°C with a space; the angle degree, attached	20 °C, 30°	20°C, 30 °
Prefix and unit are joined, and only one prefix	kW, µm, GPa	k W, mµm

Worked example · reading a line from a steel catalog

A catalog says "Rp0.2 = 355 MPa, E = 210 GPa, ρ = 7.85 g/cm³, α = 12 × 10⁻⁶ /K". Translated: the 0.2 % proof stress (yield) is 355 MPa, which is 355 N/mm² or 51.5 ksi; the modulus is 210 000 MPa, about 30 500 ksi; with ρ = 7.85 kg/dm³ a 100 × 10 mm flat bar weighs 7.85 kg per metre; and with that α, a 12 m beam grows 12 × 12 × 10⁻⁶ × 40 = 0.0058 m, almost 6 mm, between a winter morning at 0 °C and a summer afternoon at 40 °C.

Frequently asked questions

What does the Ø symbol mean on a drawing?

Diameter. It goes in front of the number (Ø25) and it is the capital O with stroke, U+00D8, typed with Alt+0216 on Windows. Argentine machinists say "fi", but the Greek φ is not written on the drawing.

How do you write micron: µm or um?

µm, with the micro sign (Alt+0181 on Windows). Writing "um" is a workaround for keyboards without the symbol, but a drawing or a data sheet should say µm. One micron is a thousandth of a millimetre, about 39 millionths of an inch.

How much is 1 MPa in kgf/cm² and in psi?

1 MPa is 10.197 kgf/cm², 145.04 psi and exactly 1 N/mm². To convert MPa to ksi, divide by 6.895: 355 MPa is 51.5 ksi.

Sources: ISO 80000-1:2022; BIPM, The International System of Units (SI Brochure), 9th edition (2019) and the 2022 resolution on the new prefixes; ISO 129-1:2018; ISO 3002; ISO 3098; RAE and ASALE, Ortografía de la lengua española (2010); The Unicode Standard.

← Appendix A: Machine shop glossary, Spanish-EnglishBook indexAppendix C: A history of the machinist's handbooks →

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Greek alphabet, SI prefixes and symbols

The Greek letters

SI prefixes

Units

Drawing and formula symbols

Roman numerals

Constants and how numbers are written

Frequently asked questions

Keep reading

Chapter 1: units and conversions

Inches to millimeters

Handbook index

A drawing full of MPa, µm and Greek letters?

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