Torque, gear ratio, beam deflection, thermal expansion, Reynolds number, hydraulic power — from statics to fluid mechanics.
Torque is the rotational equivalent of force and is fundamental in mechanical design for shafts, fasteners, motors, and structural connections. SmartFormulaPRO calculates torque through a deterministic formula engine that stores the calculation independently from spreadsheet cells, allowing engineers to reuse the same logic across different projects and components.
// --- INPUTS ---
?Force (N) [number] = force
?Moment Arm (m) [number] = arm
// --- CALCULATIONS ---
@Torque = force * arm
// --- OUTPUTS ---
#Torque (N·m) = ROUND(@Torque, 4)
Torque calculations appear repeatedly throughout mechanical design workflows. SmartFormulaPRO stores this as a reusable deterministic formula, allowing the same logic to drive consistent results across component evaluations, project phases, and engineering teams without maintaining spreadsheet copies.
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Mechanical power transmitted through a rotating shaft depends on both torque and rotational speed. This relationship is central to motor selection, gearbox design, and drivetrain analysis. SmartFormulaPRO implements this as a deterministic formula, enabling consistent power calculations across desktop environments and mobile field tools.
// --- INPUTS ---
?Torque (N·m) [number] = torque
?Rotational Speed (rpm) [number] = rpm
// --- CALCULATIONS ---
@AngularVelocity = rpm * 2 * PI() / 60
@Power = torque * @AngularVelocity
// --- OUTPUTS ---
#Angular Velocity (rad/s) = ROUND(@AngularVelocity, 4)
#Mechanical Power (W) = ROUND(@Power, 2)
#Mechanical Power (kW) = ROUND(@Power / 1000, 4)
Shaft power calculations connect torque and speed measurements into a single engineering decision point. Storing this formula inside SmartFormulaPRO keeps the calculation logic centralized and reusable across motor sizing, field verification, and mobile engineering workflows without spreadsheet dependency.
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Gear ratio determines how rotational speed and torque are transformed between two meshing gears. Mechanical engineers use this calculation for transmission design, speed reduction systems, and load matching. SmartFormulaPRO executes this through its deterministic formula engine, making the same calculation available across desktop and on-site environments.
// --- INPUTS ---
?Driver Gear Teeth [number] = driverTeeth
?Driven Gear Teeth [number] = drivenTeeth
?Driver Shaft Speed (rpm) [number] = driverSpeed
// --- CALCULATIONS ---
@GearRatio = IF(driverTeeth == 0, 0, drivenTeeth / driverTeeth)
@DrivenSpeed = IF(@GearRatio == 0, 0, driverSpeed / @GearRatio)
// --- OUTPUTS ---
#Gear Ratio = ROUND(@GearRatio, 4)
#Driven Shaft Speed (rpm) = ROUND(@DrivenSpeed, 2)
Gear ratio is one of the most reused calculations in mechanical engineering. Defining it once inside SmartFormulaPRO eliminates the need to rebuild the logic per project, supporting consistent results across transmission design, machine verification, and field deployment.
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Torsional shear stress determines whether a solid circular shaft can safely carry an applied torque without material failure. This calculation is essential during shaft design and structural verification. SmartFormulaPRO processes this through a deterministic formula engine, allowing engineering teams to run the same stress check repeatedly without rebuilding spreadsheet models.
// --- INPUTS ---
?Applied Torque (N·m) [number] = torque
?Shaft Diameter (mm) [number] = diameterMM
// --- CALCULATIONS ---
@DiameterM = diameterMM / 1000
@ShearStress = IF(@DiameterM == 0, 0, (16 * torque) / (PI() * POWER(@DiameterM, 3)))
// --- OUTPUTS ---
#Torsional Shear Stress (MPa) = ROUND(@ShearStress / 1000000, 2)
Torsional shear stress is a recurring verification step in shaft design workflows. SmartFormulaPRO centralizes this deterministic calculation so engineers can evaluate different shaft diameters and torque scenarios quickly, on desktop or mobile devices, without maintaining separate spreadsheet versions.
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Maximum deflection of a simply supported beam under a central point load is a fundamental structural check in mechanical and civil engineering. SmartFormulaPRO runs this as a deterministic formula, enabling structural engineers to evaluate different beam cross-sections and loading conditions without reconstructing the calculation in a spreadsheet.
// --- INPUTS ---
?Applied Force (N) [number] = force
?Beam Length (m) [number] = beamLength
?Elastic Modulus (GPa) [number] = elasticModulusGPa
?Moment of Inertia (cm⁴) [number] = momentCm4
// --- CALCULATIONS ---
@E = elasticModulusGPa * 1000000000
@I = momentCm4 / 100000000
@EI = @E * @I
@Deflection = IF(@EI == 0, 0, (force * POWER(beamLength, 3)) / (48 * @EI))
// --- OUTPUTS ---
#Maximum Deflection (mm) = ROUND(@Deflection * 1000, 4)
Beam deflection verification is a standard step in structural and mechanical engineering. Storing this as a deterministic formula inside SmartFormulaPRO allows the same calculation to be rerun with different material properties and section geometries, supporting consistent analysis across design iterations and field evaluations.
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Spring force is the restoring force produced by an elastic spring deformed from its natural length. Described by Hooke's Law, this calculation is used in mechanical product design, vibration isolation, and component testing. SmartFormulaPRO stores this as a deterministic formula that can be executed consistently across engineering workflows.
// --- INPUTS ---
?Spring Constant (N/m) [number] = springConstant
?Displacement (mm) [number] = displacementMM
// --- CALCULATIONS ---
@DisplacementM = displacementMM / 1000
@SpringForce = springConstant * @DisplacementM
// --- OUTPUTS ---
#Spring Force (N) = ROUND(@SpringForce, 4)
Hooke's Law is one of the most frequently applied relationships in mechanical engineering. Defining spring force once inside SmartFormulaPRO eliminates per-project spreadsheet rebuilding and supports consistent evaluation of spring-loaded mechanisms across desktop and mobile environments.
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Thermal expansion must be accounted for in structures, pipelines, rails, engine components, and precision machinery when operating across temperature ranges. SmartFormulaPRO calculates linear thermal expansion through a deterministic formula engine, enabling engineers to evaluate dimensional changes consistently without maintaining separate calculation worksheets.
// --- INPUTS ---
?Thermal Expansion Coefficient (10⁻⁶ /°C) [number] = alphaMicro
?Original Length (m) [number] = originalLength
?Temperature Change (°C) [number] = deltaT
// --- CALCULATIONS ---
@Alpha = alphaMicro / 1000000
@Expansion = @Alpha * originalLength * deltaT
@NewLength = originalLength + @Expansion
// --- OUTPUTS ---
#Thermal Expansion (mm) = ROUND(@Expansion * 1000, 4)
#New Length (m) = ROUND(@NewLength, 6)
Thermal expansion calculations protect structures and mechanical components from dimensional interference caused by temperature variation. Storing this deterministic formula inside SmartFormulaPRO allows the same logic to be applied to different materials and temperature ranges, supporting consistent design decisions across engineering disciplines.
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Volumetric flow rate through a circular pipe depends on pipe cross-sectional area and average flow velocity. This calculation is used in hydraulic system design, HVAC, water supply, and industrial fluid transport. SmartFormulaPRO executes this as a deterministic formula, allowing fluid engineers to evaluate different pipe diameters and flow velocities consistently.
// --- INPUTS ---
?Pipe Inner Diameter (mm) [number] = diameterMM
?Flow Velocity (m/s) [number] = velocity
// --- CALCULATIONS ---
@DiameterM = diameterMM / 1000
@CrossSection = PI() * POWER(@DiameterM, 2) / 4
@FlowRateM3s = @CrossSection * velocity
// --- OUTPUTS ---
#Pipe Cross-Section (m²) = ROUND(@CrossSection, 8)
#Flow Rate (m³/s) = ROUND(@FlowRateM3s, 6)
#Flow Rate (L/min) = ROUND(@FlowRateM3s * 60000, 2)
Pipe flow rate is calculated repeatedly across hydraulic and fluid systems engineering. SmartFormulaPRO stores the formula as a reusable deterministic definition, removing the need to rebuild the logic in spreadsheet cells for each new pipe diameter or velocity scenario, and supporting consistent results across field and desktop workflows.
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The Reynolds number classifies pipe flow as laminar, transitional, or turbulent based on fluid properties and flow conditions. This dimensionless parameter is critical in heat exchanger design, pump selection, and fluid system analysis. SmartFormulaPRO calculates Reynolds number through a deterministic formula that engineers can reuse consistently across projects.
// --- INPUTS ---
?Fluid Density (kg/m³) [number] = density
?Flow Velocity (m/s) [number] = velocity
?Pipe Inner Diameter (m) [number] = diameter
?Dynamic Viscosity (Pa·s) [number] = viscosity
// --- CALCULATIONS ---
@Reynolds = IF(viscosity == 0, 0, (density * velocity * diameter) / viscosity)
// --- OUTPUTS ---
#Reynolds Number = ROUND(@Reynolds, 0)
Reynolds number is evaluated at every stage of fluid system design. Defining this calculation once inside SmartFormulaPRO removes the need to rebuild it in spreadsheets for each project, supporting consistent flow regime classification across hydraulic design, field analysis, and engineering review.
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Compression ratio determines how much the fuel-air mixture is compressed inside an engine cylinder before ignition, directly affecting engine efficiency and power output. SmartFormulaPRO calculates compression ratio through a deterministic formula that automotive and mechanical engineers can reuse across different engine configurations.
// --- INPUTS ---
?Swept Volume per Cylinder (cc) [number] = sweptVolume
?Clearance Volume per Cylinder (cc) [number] = clearanceVolume
// --- CALCULATIONS ---
@CompressionRatio = IF(clearanceVolume == 0, 0, (sweptVolume + clearanceVolume) / clearanceVolume)
// --- OUTPUTS ---
#Compression Ratio = ROUND(@CompressionRatio, 2)
Compression ratio is a defining parameter in every internal combustion engine design. Storing this calculation as a deterministic formula inside SmartFormulaPRO allows engineers to evaluate multiple cylinder configurations quickly, supporting consistent analysis across engine development, performance tuning, and field verification.
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Centrifugal force acts on rotating masses and must be considered in the design of flywheels, centrifuges, rotating machinery, and vehicle dynamics systems. SmartFormulaPRO calculates centrifugal force using a deterministic formula engine that converts rotational speed to angular velocity and evaluates the resulting outward force consistently.
// --- INPUTS ---
?Mass (kg) [number] = mass
?Rotation Radius (m) [number] = radius
?Rotational Speed (rpm) [number] = rpm
// --- CALCULATIONS ---
@AngularVelocity = rpm * 2 * PI() / 60
@CentrifugalForce = mass * POWER(@AngularVelocity, 2) * radius
// --- OUTPUTS ---
#Angular Velocity (rad/s) = ROUND(@AngularVelocity, 4)
#Centrifugal Force (N) = ROUND(@CentrifugalForce, 2)
#Centrifugal Force (kN) = ROUND(@CentrifugalForce / 1000, 4)
Centrifugal force is evaluated during the design of every rotating mechanical assembly. SmartFormulaPRO keeps this calculation centralized and reusable, allowing engineers to test different mass distributions and rotational speeds without rebuilding the logic in spreadsheets for each scenario.
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Belt drives transmit power between parallel shafts and are widely used in industrial machines, HVAC systems, and automotive engines. Driven pulley speed and belt velocity are the primary design parameters. SmartFormulaPRO calculates both through a deterministic formula engine, providing consistent results across machine design and verification workflows.
// --- INPUTS ---
?Driver Pulley Diameter (mm) [number] = driverDiameter
?Driven Pulley Diameter (mm) [number] = drivenDiameter
?Driver Pulley Speed (rpm) [number] = driverSpeed
// --- CALCULATIONS ---
@DrivenSpeed = IF(drivenDiameter == 0, 0, driverSpeed * driverDiameter / drivenDiameter)
@BeltVelocity = PI() * (driverDiameter / 1000) * driverSpeed / 60
// --- OUTPUTS ---
#Driven Pulley Speed (rpm) = ROUND(@DrivenSpeed, 2)
#Belt Velocity (m/s) = ROUND(@BeltVelocity, 4)
Belt drive calculations are repeated across every machine configuration that uses pulley power transmission. Defining speed ratio and belt velocity once inside SmartFormulaPRO eliminates spreadsheet duplication and supports consistent design decisions across machine engineering and on-site installation verification.
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Pump power depends on fluid density, flow rate, delivery head, and pump efficiency. This calculation is used in water supply systems, hydraulic machinery, chemical processing, and industrial plant design. SmartFormulaPRO executes this as a deterministic formula engine calculation, allowing engineers to size pumps consistently without maintaining spreadsheet models.
// --- INPUTS ---
?Fluid Density (kg/m³) [number] = density
?Flow Rate (m³/h) [number] = flowRateM3h
?Total Head (m) [number] = head
?Pump Efficiency (%) [number] = efficiency
// --- CALCULATIONS ---
@FlowRateM3s = flowRateM3h / 3600
@HydraulicPower = density * 9.81 * @FlowRateM3s * head
@EfficiencyDecimal = IF(efficiency == 0, 1, efficiency / 100)
@ShaftPower = IF(@EfficiencyDecimal == 0, 0, @HydraulicPower / @EfficiencyDecimal)
// --- OUTPUTS ---
#Hydraulic Power (W) = ROUND(@HydraulicPower, 2)
#Required Shaft Power (kW) = ROUND(@ShaftPower / 1000, 4)
Pump power calculation is repeated across every hydraulic and fluid system engineering project. Storing this formula inside SmartFormulaPRO allows the same deterministic logic to evaluate different pump configurations, fluid types, and efficiency values consistently, supporting both office design and mobile field verification.
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Heat conduction through a flat wall is described by Fourier's Law and is essential in thermal insulation design, heat exchanger engineering, and industrial process analysis. SmartFormulaPRO calculates steady-state heat transfer rate as a deterministic formula, allowing thermal engineers to evaluate different material and geometry combinations without rebuilding spreadsheet models.
// --- INPUTS ---
?Thermal Conductivity (W/m·K) [number] = conductivity
?Surface Area (m²) [number] = area
?Hot Side Temperature (°C) [number] = tempHot
?Cold Side Temperature (°C) [number] = tempCold
?Wall Thickness (m) [number] = thickness
// --- CALCULATIONS ---
@TempDiff = tempHot - tempCold
@HeatRate = IF(thickness == 0, 0, conductivity * area * @TempDiff / thickness)
// --- OUTPUTS ---
#Temperature Difference (°C) = ROUND(@TempDiff, 2)
#Heat Transfer Rate (W) = ROUND(@HeatRate, 2)
#Heat Transfer Rate (kW) = ROUND(@HeatRate / 1000, 4)
Fourier's Law of heat conduction underpins thermal analysis across construction, manufacturing, and process engineering. Defining this as a reusable deterministic formula inside SmartFormulaPRO allows engineers to compare different insulation materials, thicknesses, and temperature gradients quickly without reconstructing calculation sheets.
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The natural frequency of a mass-spring system determines the frequency at which the system resonates. Avoiding resonance is critical in vibration engineering, machine design, structural dynamics, and noise control. SmartFormulaPRO calculates natural frequency and oscillation period through a deterministic formula, providing consistent results for vibration analysis across engineering applications.
// --- INPUTS ---
?Spring Stiffness (N/m) [number] = stiffness
?Vibrating Mass (kg) [number] = mass
// --- CALCULATIONS ---
@StiffnessMassRatio = IF(mass == 0, 0, stiffness / mass)
@OmegaN = IF(@StiffnessMassRatio <= 0, 0, SQRT(@StiffnessMassRatio))
@NaturalFrequency = IF(@OmegaN == 0, 0, @OmegaN / (2 * PI()))
@Period = IF(@NaturalFrequency == 0, 0, 1 / @NaturalFrequency)
// --- OUTPUTS ---
#Natural Angular Frequency (rad/s) = ROUND(@OmegaN, 4)
#Natural Frequency (Hz) = ROUND(@NaturalFrequency, 4)
#Oscillation Period (s) = ROUND(@Period, 4)
Natural frequency is a fundamental property evaluated in every dynamic mechanical system. Storing this calculation inside SmartFormulaPRO allows vibration engineers to quickly evaluate different stiffness and mass combinations across design iterations, supporting consistent resonance avoidance analysis on desktop and mobile platforms.
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