What is engineering?
Engineering is the disciplined application of mathematics,
science, and practical experience to design, build, and maintain
systems that solve real‑world problems. Unlike pure science,
which focuses on understanding how the world works, engineering
focuses on creating things that work reliably, safely, and
efficiently.
Major branches include:
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Civil & structural engineering –
buildings, bridges, roads, foundations, water and wastewater
systems.
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Mechanical engineering – machines, vehicles,
HVAC, manufacturing, thermodynamics, and fluid mechanics.
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Electrical and electronics engineering –
power generation and distribution, electronics, control
systems, communications.
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Chemical & process engineering – chemical
plants, reactors, separation processes, energy and mass
transfer.
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Systems, software, and industrial engineering
– complex systems, optimization, reliability, operations, and
automation.
Core engineering relationships and formulas
Many engineering calculators on this site are built around a
small set of fundamental physical relationships. Understanding
these helps you interpret any result.
1. Conservation of mass
For a steady‑state system with one inlet and one outlet:
\[ \dot{m}_{\text{in}} = \dot{m}_{\text{out}} \]
where \(\dot{m}\) is mass flow rate (e.g. kg/s).
In more complex systems, the general form is:
\[ \frac{d m_{\text{system}}}{dt} = \sum \dot{m}_{\text{in}} -
\sum \dot{m}_{\text{out}} \]
2. Newton’s second law (mechanics)
\[ \sum \vec{F} = m \vec{a} \] where \(\sum \vec{F}\) is the sum
of forces, \(m\) is mass, and \(\vec{a}\) is acceleration.
This underpins structural analysis (internal forces and
moments), vibration, and dynamics calculators.
3. Stress and strain
Normal stress: \[ \sigma = \frac{F}{A} \] Strain: \[ \varepsilon
= \frac{\Delta L}{L_0} \] Hooke’s law (linear elastic region):
\[ \sigma = E \varepsilon \]
Here \(F\) is axial force, \(A\) is cross‑sectional area,
\(\Delta L\) is change in length, \(L_0\) is original length,
and \(E\) is Young’s modulus.
4. Energy and power
Mechanical work: \[ W = F \cdot s \] Power: \[ P = \frac{dW}{dt}
\] Electrical power (DC): \[ P = V I \]
Many calculators convert between mechanical, electrical, and
thermal power units (W, hp, BTU/hr, etc.).
5. Fluid flow and Reynolds number
Reynolds number: \[ \mathrm{Re} = \frac{\rho V D}{\mu} \] where
\(\rho\) is density, \(V\) is mean velocity, \(D\) is
characteristic length (e.g. pipe diameter), and \(\mu\) is
dynamic viscosity.
\(\mathrm{Re}\) determines whether flow is laminar or turbulent
and influences friction factors and pressure drop.
6. Ohm’s law and impedance
Ohm’s law: \[ V = I R \] For AC circuits, impedance \(Z\)
generalizes resistance: \[ V = I Z \]
Electrical calculators extend this to three‑phase systems, power
factor, and frequency‑dependent reactance.
How to use engineering calculators effectively
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Define the problem clearly. Identify what you
need to solve for (e.g. required beam size, pressure drop,
motor power).
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Gather realistic input data. Use appropriate
units, material properties, and safety factors from standards
or datasheets.
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Check units and ranges. If a result looks
unreasonable, verify units and input magnitudes first.
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Use calculators as decision support, not as the only
authority.
Final designs should be checked against the latest codes and
reviewed by a qualified engineer.
FAQ about engineering & these tools
Is engineering more about math or creativity?
Both. Math and physics provide the constraints and quantitative
checks; creativity and judgment are needed to choose concepts,
simplify problems, and balance trade‑offs such as cost, safety,
and performance.
Can these calculators replace professional engineering software?
No. They are ideal for quick checks, education, and early‑stage
design, but they do not replace full finite‑element models,
detailed code checks, or multi‑discipline coordination. Think of
them as fast, transparent tools that complement heavier
software.
Where do the formulas come from?
The formulas are drawn from standard engineering textbooks,
widely used design codes (ACI, AISC, ASCE, Eurocodes, NEC, BS
7671, etc.), and peer‑reviewed references. Each individual
calculator page cites the specific assumptions and equations it
uses.