Unit System

EngCanvas's unit system tracks four fundamental dimensions — Length (L), Mass (M), Time (T), and Force (F) — through every arithmetic operation. This page covers the internals of how dimensional analysis works.

The four dimensions

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

Every unit in the registry maps to a combination of these four dimensions. For example:

Unit	L	M	T	F	Physical meaning
ft	1	0	0	0	Length
kip	0	0	0	1	Force
psi	-2	0	0	1	Force / Length² (pressure)
pcf	-3	0	0	1	Force / Length³ (unit weight)
mph	1	0	-1	0	Length / Time (velocity)
kg	0	1	0	0	Mass

Force vs. mass

EngCanvas treats force and mass as independent dimensions. This differs from the SI convention (where force = mass × acceleration) but matches how structural engineers think. lb is a force (F=1), while lb_m is a mass (M=1).

How conversions work

All arithmetic happens in SI units internally:

1. Input: your value is converted to SI using the toSI factor
2. Calculate: arithmetic in SI
3. Output: result converted back using the fromSI factor

// Example: 10 ft + 36 in
// Step 1: 10 × 0.3048 = 3.048 m,  36 × 0.0254 = 0.9144 m
// Step 2: 3.048 + 0.9144 = 3.9624 m
// Step 3: 3.9624 ÷ 0.3048 = 13.0 ft
// Result: 13 ft

This SI-first approach means you can freely mix unit systems:

total = 1 m + 12 in + 2 ft

Dimension rules for operations

Addition / Subtraction

Both operands must have identical dimensions:

10 ft + 3 in        ✓  (both L=1)
50 kip - 10 kip     ✓  (both F=1)
10 ft + 5 kip       ✗  (L=1 ≠ F=1)

Multiplication

Dimensions add:

10 kip × 3 ft = 30 kip·ft     // F=1, L=1 → moment
4 ft × 6 ft = 24 ft^2         // L=1 + L=1 → L=2 (area)

Division

Dimensions subtract:

100 kip / 20 in^2 = 5 ksi     // F=1, L=-2 → pressure
24 ft / 2 sec = 12 fps        // L=1, T=-1 → velocity

Exponentiation

Dimensions scale:

(4 ft)^2 = 16 ft^2            // L=1 × 2 → L=2
(2 m)^3 = 8 m^3               // L=1 × 3 → L=3

Comparison

Operands should have the same dimensions. The comparison returns a dimensionless boolean:

10 ft > 100 in                 // ✓ both are length → true (10 ft = 120 in)

Compound unit syntax

Combine base units for complex quantities:

Syntax	Meaning	Dimensions
kip·ft	Force × length	F=1, L=1
lb/ft^3	Force / length³	F=1, L=-3
kN/m^2	Force / length²	F=1, L=-2
lb·ft/s^2	Force × length / time²	F=1, L=1, T=-2

Use · (middle dot) or * for multiplication between units, and / for division.

Unit powers

Attach ^n to any unit:

500 in^4         // moment of inertia (L⁴)
12 ft^2          // area (L²)
27 ft^3          // volume (L³)
3 m^-1           // inverse length
2 ft^0.5         // square root of length (decimal powers supported)

Complete unit registry

All 46 built-in units, grouped by dimension.

Length (L=1)

m, ft, in, mm, cm, km, yd, mi, mil

Force (F=1)

N, kN, MN, lb, lbs, kip

Mass (M=1)

kg, gm, mg, ton, lb_m

Pressure (F=1, L=-2)

Pa, kPa, MPa, GPa, psi, psf, ksi, ksf

Time (T=1)

s, sec, min, hr

Angle (dimensionless)

deg, rad

Temperature (dimensionless, affine)

degK, degC, degF

Temperatures are the one affine family: converting to SI applies an offset as well as a scale, valueSI = value × toSI + offset. So 0 degC is 273.15 degK, not 0 degK.

The offset is applied only at power 1. degC^2 has no meaningful affine interpretation, so it converts multiplicatively like any other unit.

The names are spelled degK/degC/degF rather than K/C/F because every registry key tokenizes as a unit, and a bare K, C, or F would shadow the engineering variable names those letters usually stand for.

Velocity (L=1, T=-1)

mph, fps

Acceleration (L=1, T=-2)

g (standard gravity = 9.80665 m/s²)

Volume (L=3)

L (liter), gal (US gallon), bu (US bushel)

Unit weight (F=1, L=-3)

pcf (lb/ft³), pci (lb/in³), kcf (kip/ft³)

Dimensionless quantities

Some results are dimensionless — their dimension vector is {L:0, M:0, T:0, F:0}:

ratio = fb / Fb                // stress / stress → dimensionless
angle = 45 deg                 // angles are dimensionless
count = COUNT($A1:$A10)        // pure number

Error detection

EngCanvas catches these dimensional errors:

Error	Example	Problem
Mismatched add/subtract	10 ft + 5 kip	Length ≠ Force
Unknown unit	10 xyz	xyz not in registry
Invalid conversion	converting kip to ft	Force ≠ Length

Next steps

• Working with Units — practical unit guide
• Operators — how operators interact with dimensions