Engineering Unit Conversion - A Structural Reference

Consistent units are the foundation of every structural calculation - a single unit slip turns a safe design into a dangerous one. This reference sets out the SI system used throughout Eurocode work, the derived units for the quantities engineers handle daily, and the conversions and common traps the converter helps you avoid.

SI base and derived units

The SI system is built on seven base units; structural work uses three of them - the metre (m), kilogram (kg) and second (s) - and a set of derived unitsformed from them. Force is the key one: by Newton's second law a newton is the force that accelerates one kilogram at one metre per second squared:

Force - newtons, kilonewtons and kgf

Structural loads are usually in kilonewtons (kN). The frequent confusion is the old kilogram-force(kgf, or just “kg” of load in older drawings): a kilogram-force is the weight of one kilogram under standard gravity, so it is not a kilogram:

Treating a kgf as a newton (or a tonne-force as a kN) understates a load by a factor of about 9.81 - a classic and dangerous mistake when reading older or mixed-unit documents.

Pressure and stress - the MPa = N/mm² identity

Pressure and stress share units. The single most useful identity in structural units is that a megapascal equals a newton per square millimetre - because the million in “mega” exactly cancels the million in (1000 mm)²:

So a concrete grade C30/37 ($f_{ck} = 30$ MPa) is 30 N/mm², and a steel yield of 355 MPa is 355 N/mm². Other pressure units still appear: 1 bar = 100 kPa, 1 atm ≈ 101.3 kPa, and 1 psi ≈ 6.895 kPa.

Moment, area and section properties

Bending moments are force times distance - kN·m in design. Section properties carry powers of length, so unit care matters:

Section tables list $I$ in cm⁴ and $W$ in cm³, but capacity formulas need consistent units - convert to N and mm (or kN and m) throughout a calculation and never mix.

Working safely with units

• Pick one consistent system for a calculation - most Eurocode work uses N and mm (so stresses come out in MPa directly) or kN and m.
• Carry units through every step; if the units of the result are wrong, the arithmetic is wrong.
• Watch the kgf/tonne-force traps in older or non-SI documents - multiply by ~9.81 to get newtons.
• Remember MPa = N/mm² and kPa = kN/m² - the two identities that remove most pressure/stress confusion.

The converter handles length, area, volume, force, pressure/stress, moment, distributed load and density across SI and imperial units, so you can move between systems without arithmetic slips.