Working with Units

Units are central to EngCanvas. Every quantity carries dimensional metadata, arithmetic propagates dimensions automatically, and incompatible operations are flagged at evaluation time.

Attaching units to numbers

Place the unit immediately after the number:

L = 20 ft
F = 10 kip
P = 3000 psi
t = 5 sec

EngCanvas recognizes 46 built-in units across eleven categories. Beyond these you can combine any of them into compound units — see Compound units below.

Unit categories

Length

Unit	Description
m	Meter (SI base)
ft	Foot
in	Inch
mm, cm, km	Millimeter, centimeter, kilometer
yd	Yard
mi	Mile
mil	Thousandth of an inch

Force

Unit	Description
N	Newton (SI base)
kN, MN	Kilonewton, meganewton
lb, lbs	Pound-force
kip	Kilopound (1000 lb)

Mass

Unit	Description
kg	Kilogram (SI base)
gm	Gram
mg	Milligram
ton	Metric ton (1000 kg)
lb_m	Pound-mass

Pressure / Stress

Unit	Description
Pa, kPa, MPa, GPa	Pascal and multiples
psi	Pounds per square inch
psf	Pounds per square foot
ksi	Kips per square inch
ksf	Kips per square foot

Time

Unit	Description
s, sec	Second (SI base)
min	Minute
hr	Hour

Angle

Unit	Description
rad	Radian (SI base)
deg	Degree

Temperature

Unit	Description
degK	Kelvin (SI base)
degC	Degree Celsius
degF	Degree Fahrenheit

Temperature units are affine

Unlike every other unit, temperatures convert with an offset as well as a scale (degC → K adds 273.15). Write degK, not K — a bare K would shadow common variable names. The offset is applied only at power 1, so degC^2 is treated as a plain multiplicative unit rather than a temperature.

Velocity

Unit	Description
mph	Miles per hour
fps	Feet per second

Volume

Unit	Description
L	Liter
gal	US gallon
bu	US bushel

Unit weight (force per volume)

Unit	Description
pcf	Pounds per cubic foot (lb/ft³)
pci	Pounds per cubic inch (lb/in³)
kcf	Kips per cubic foot (kip/ft³)

Other

Unit	Description
g	Standard gravity (9.80665 m/s²)

Compound units

Combine units with · (multiplication) and / (division):

stress = 10 kN/m^2       // pressure
moment = 50 kip·ft        // force × length
unitWt = 150 lb/ft^3      // unit weight

Add exponents with ^:

I = 500 in^4              // moment of inertia
A = 12 in^2               // area (same as in^2)

How unit arithmetic works

Multiplication

Dimensions add:

F = 10 kip
d = 3 ft
M = F * d                 // → 30 kip·ft (F·L)

Division

Dimensions subtract:

P = 100 kip
A = 20 in^2
stress = P / A             // → 5 ksi (F/L²)

Addition and subtraction

Dimensions must match. These work:

total = 10 ft + 36 in      // → 13 ft (both are length)
net = 50 kip - 10 kip      // → 40 kip (both are force)

This raises an error:

bad = 10 ft + 5 kip        // ✗ Dimension mismatch: L ≠ F

Exponentiation

Dimensions scale:

side = 4 ft
area = side^2              // → 16 ft^2 (L²)
volume = side^3            // → 64 ft^3 (L³)

Dimensional analysis (L, M, T, F)

Every unit maps to four fundamental dimensions:

Symbol	Dimension	SI base unit
L	Length	meter (m)
M	Mass	kilogram (kg)
T	Time	second (s)
F	Force	newton (N)

Examples:

Quantity	Dimensions	Example units
Length	L¹	ft, m, in
Area	L²	ft^2, m^2
Volume	L³	ft^3, m^3
Force	F¹	kip, N, lb
Pressure	F¹·L⁻²	psi, kPa, MPa
Moment	F¹·L¹	kip·ft, N·m
Unit weight	F¹·L⁻³	pcf, kcf
Velocity	L¹·T⁻¹	mph, fps

Force vs. Mass

EngCanvas tracks force (F) and mass (M) as independent dimensions. This avoids the confusion between pound-force (lb, F=1) and pound-mass (lb_m, M=1). Use lb for forces and lb_m when you specifically mean mass.

Unit conversion through SI

All calculations happen internally in SI units. The flow is:

1. Input: 10 ft → convert to SI → 3.048 m
2. Calculate: all math in SI
3. Output: convert from SI → display in the unit you wrote

This means you can freely mix unit systems:

total = 1 m + 12 in        // → 1.3048 m (or equivalently, 4.28 ft)

Next steps

• Unit System (deep dive) — dimensional analysis internals
• Operators — how operators interact with units