Engineering is built on formulas. Whether you are designing a control loop, calculating fluid flow through a pipe, or troubleshooting a transmitter in the instrumentation field, the right equation can save both time and costly mistakes.
For engineers and supervisors in instrumentation and process industries, these formulas are not just academic they are practical tools used every single day.
This guide brings together 100 essential engineering formulas, carefully selected and structured for quick reference.
From pressure, flow, and temperature calculations to electrical, control system, and measurement formulas, each equation is presented with context, field applications, and quick tips to make it easier to apply in real world situations.
This handbook you can keep by your side, whether you are on site, in the control room, or mentoring new engineers. By mastering these formulas, you will not only improve accuracy in calculations but also gain confidence in decision making, design, and troubleshooting.
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| Basic Pressure |  | Pressure equals Force divided by Area. Used in all pressure instruments (gauges, transmitters). |
| Hydrostatic Pressure |  | Pressure due to liquid column. Basis of DP transmitters for level measurement. Rule: Water density ≈ 1000 kg/m³, g = 9.81 m/s². |
| Differential Pressure (general) |  | Difference between two pressure points. Core of DP flow measurement (orifice, venturi, nozzle). |
| Absolute Pressure |  | Absolute pressure includes atmospheric pressure. Used in vacuum systems, boilers. |
| Gauge Pressure |  | Pressure relative to atmosphere. What most pressure gauges display. |
| Unit Conversion (bar → Pa) |  | Quick conversion. Rule: 1 bar ≈ 14.5 psi. |
| Unit Conversion (psi → Pa) |  | Common in oil & gas. Rule: 100 psi ≈ 6.9 bar. |
| Liquid Level (from pressure) |  | Height of liquid based on hydrostatic pressure. Used in tank level transmitters. |
| Level from DP transmitter |  | Linearized relation between level and DP. Calibration constant CC depends on tank geometry. |
| Tank Volume (cylindrical) |  | Volume of a vertical cylindrical tank. Used in storage tank gauging. |
| Tank Height (cylindrical) |  | Calculates level from tank volume. |
| Tank Volume (rectangular) |  | Volume of rectangular/square tanks. |
| Level Change over Time |  | Level rise/fall = rate × time. Used in pump performance checks. |
| DP from Liquid Column |  | Core of all DP level measurements. Quick tip: For water, 10 m height ≈ 1 bar. |
| Absolute vs Gauge Example |  | At sea level, add 1 atm (101.3 kPa) to hydrostatic. Example: 5 m water column → ~150 kPa absolute. |
Flow: Engineering Formulas
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| Continuity Equation |
| Volumetric flow rate = cross-sectional area × velocity. Used in all closed-pipe flow calculations. |
| Mass Flow Rate |  | Mass flow = density × volumetric flow. Essential in custody transfer and chemical dosing. |
| Flow in Circular Pipe |
| Flow rate using diameter and velocity. |
| Total Volume |  | Volume over time = flow rate × time. Used in batching and dosing applications. |
| Bernoulli’s Equation |
| Energy conservation in fluids. Basis of venturi, pitot tube, and nozzle meters. |
| Orifice Flow Equation |  | Flow rate from pressure drop across an orifice plate. Still industry standard in oil & gas custody transfer. |
| Venturi Flow Equation |  | Venturi meters used in water, wastewater, and chemical plants. Less permanent pressure loss than orifice plates. |
| Pitot Tube Velocity |  | Measures velocity using static and dynamic pressure. Used in HVAC ducts, aircraft, and large pipes. |
| Hagen–Poiseuille Law (Laminar Flow) |  | Flow through small tubes in laminar regime. Rule: Valid only if Re<2000Re < 2000. |
| Reynolds Number |  | Dimensionless number to classify flow. Rule: Re < 2000 → Laminar, Re > 4000 → Turbulent. |
| Darcy–Weisbach Equation (Head Loss) |  | Head loss due to friction in pipes. Rule: For water, pressure drop ≈ 0.1 bar per 10 m in clean pipes. |
| Weir Flow (Rectangular) |  | Open channel flow (rectangular notch). Used in water treatment plants. |
| Weir Flow (V-Notch) |  | Open channel flow with V-notch. Very sensitive at low flow rates. |
| Faraday’s law |  | Induced EMF ∝ velocity. Works only for conductive liquids (> 5 µS/cm). |
| Coriolis Mass Flow |  | Coriolis force deflects vibrating tubes. Direct mass flow measurement in oil, gas, chemicals. |
Temperature: Engineering Formulas
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| Celsius to Fahrenheit |  | Temperature unit conversion. Widely used in instrumentation calibration manuals (US equipment often uses °F). |
| Fahrenheit to Celsius |  | Reverse conversion. |
| Celsius to Kelvin |  | Absolute temperature scale. Required in thermodynamics and gas laws. |
| Kelvin to Celsius |  | Reverse conversion. |
| Temperature Rise (Heat Transfer) |  | Heat added raises temperature depending on mass and specific heat. Used in heat exchanger sizing. |
| Heat Conduction (Fourier’s Law) |  | Heat flow through solids. Used for thermowell design and insulation. |
| Heat Convection (Newton’s Law of Cooling) |  | Heat transfer between surface and fluid. Common in furnaces, boilers, cooling coils. |
| Heat Radiation (Stefan–Boltzmann Law) |  | Radiative heat transfer. Used in furnaces and high-temperature processes. |
| Thermocouple EMF (Seebeck Effect) |  | Voltage generated proportional to temperature difference. Used in thermocouple calibration; S = Seebeck coefficient. |
| RTD Resistance–Temperature Relation |  | Resistance increases linearly with temperature. For Pt100, α=0.00385\alpha = 0.00385. |
| Wien’s Law (Blackbody Radiation Peak) |  | Wavelength of peak emission inversely proportional to temperature. Used in infrared temperature measurement. |
| Thermal Expansion (Linear) |  | Length change due to temperature rise. Must be considered in sensor installation. |
| Thermal Expansion (Volume) |  | Volume change with temperature rise. |
| Enthalpy Change |  | Energy required at constant pressure. Steam tables use this relation. |
| Steady-State Heat Balance |  | For steady processes, input heat = output heat. Used in furnace and exchanger balance. |
Electrical: Engineering Formulas
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| Ohm’s Law |  | Voltage = Current × Resistance. Basis of all electrical instrumentation. |
| Power (General) |  | Electrical power. Used for sizing power supplies in instrumentation systems. |
| Power (Resistive Load) |  | Power dissipation in resistors. Used in heat generation estimation. |
| Power (from Voltage & Resistance) |  | Alternative power formula. |
| Energy Consumed |  | Energy = Power × Time. Used in energy meters (kWh). |
| Charge (Coulomb’s Law) |  | Charge flow = Current × Time. |
| Capacitance Definition |  | Capacitance = Charge per voltage. |
| Inductive Reactance |  | Opposition to AC by inductors. Key in solenoids, transformers. |
| Capacitive Reactance |  | Opposition to AC by capacitors. |
| Impedance (RLC Circuit) |  | Total AC resistance. Used in signal filtering. |
| Frequency |  | Frequency is reciprocal of time period. 50 Hz / 60 Hz mains systems. |
| Resistivity Formula |  | Resistance depends on material, length, and area. Important in cable sizing. |
| AC Power (Single-Phase) |  | Real power in AC circuit. |
| AC Power (Three-Phase) |  | Three-phase power calculation. Used in industrial motors and drives. |
| Transformer Equation |  | Voltage ratio proportional to turns ratio. Key in instrument transformers (CTs, PTs). |
Control Systems: Engineering Formulas
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| Error Signal |  | Error = Setpoint – Process Value. Basis of all control actions. |
| Proportional Gain |  | Output change per unit error. Higher KpK_p = faster response but risk of oscillation. |
| PID Controller |  | Standard control law. Widely used in process automation (flow, pressure, temperature loops). |
| PI Controller |  | Eliminates steady-state error. |
| PD Controller |  | Improves stability and response speed. |
| Transfer Function |  | System behavior in Laplace domain. Used in stability analysis. |
| Closed-Loop Transfer Function |  | Overall response including feedback. |
| First-Order Time Constant |  | Time constant of a first-order system. Example: RC circuits, temperature sensors. |
| Natural Frequency |  | Frequency of undamped oscillations. |
| Damping Ratio |  | Determines if system is underdamped, critically damped, or overdamped. |
| Percent Overshoot |  | Maximum overshoot in step response. |
| Settling Time (2% criterion) |  | Time to settle within 2% of final value. |
| Rise Time |  | Speed of system reaching target. |
General Engineering & Measurement Formulas
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| Density |  | Mass per unit volume. Used in flow, level, and custody transfer. |
| Specific Gravity (SG) |  | Dimensionless ratio vs. water. Rule: SG = 1 for water at 4 °C. |
| Weight (Force) |  | Force due to gravity. Often used in load cells and gravimetric feeders. |
| Pressure Head |  | Converts pressure into liquid column height. |
| Velocity Head |  | Energy in moving fluid. Part of Bernoulli’s equation. |
| Power (Mechanical) |  | Mechanical power from force and velocity. |
| Efficiency |  | System efficiency in %. Rule: Pumps and compressors typically 60–80%. |
| Work Done |  | Work = Force × Distance moved. |
| Stress |  | Force per unit area. Important in pressure vessel design. |
| Strain |  | Deformation per unit length. Used with strain gauges. |
| Hooke’s Law |  | Stress proportional to strain (within elastic limit). |
| Percentage Error |  | Accuracy evaluation in calibration. |
| Absolute Error |  | The magnitude of the difference between the measured value and the actual (true) value. |
| Relative Error |  | Normalized error relative to true value. |
| Standard Deviation |  | Statistical spread of measurements. Used in instrument repeatability tests. |
Advanced Instrumentation Engineering Formulas
| Formula & Name | Equation | Description / Industry Context / Quick Tip |
|---|---|---|
| 4–20 mA Signal Conversion |  | Converts process variable to standard transmitter output. Example: 50% PV = 12 mA. |
| Percent of Span (Signal) |  | Shows where the process variable lies within calibrated range. |
| Voltage Divider |  | Used in sensor conditioning circuits. |
| Wheatstone Bridge Balance |  | Basis of strain gauge, RTD, and pressure transducers. |
| Signal-to-Noise Ratio (SNR) |  | Ratio of signal to noise strength. Higher SNR → better measurement accuracy. |
| Noise Voltage (Thermal) |  | Johnson noise in resistors. Important in low-level signal sensors. |
| Uncertainty (Root-Sum-Square) |  | Total uncertainty from multiple sources. |
| Tolerance |  | Instrument accuracy specification. |
| Resolution |  | Smallest measurable change relative to span. |
| Time Constant (First-Order Sensor) |  | Response speed of temperature sensors, pressure transmitters, etc. Rule: Sensor reaches 63.2% of step change in 1 τ. |
| Damping Ratio (Sensor Response) |  | Defines if sensor is overdamped, underdamped, or critically damped. |
| Bandwidth |  | Frequency response limit of sensors. |
| Span of Instrument |  | Difference between Upper & Lower Range Values. |
| Rangeability (Turndown Ratio) |  | Ability of an instrument to measure across wide ranges. Example: Orifice meters typically 3:1, Coriolis meters 100:1. |
| Calibration Error (%) |  | Used in calibration reports to evaluate deviation. |
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