Axial Stress
Calculates the normal stress on a member subjected to an axial load.
Flexural Stress (Bending)
Calculates the bending stress at a distance y from the neutral axis.
Transverse Shear Stress in Beams
Calculates the shear stress at a specific layer in a beam cross-section.
Torsional Shear Stress (Circular Shaft)
Calculates the shear stress due to torsion in a circular shaft.
Euler's Critical Buckling Load
Calculates the critical axial load that will cause a column to buckle.
Deflection of SS Beam (Uniform Load)
Maximum deflection of a simply supported beam with a uniformly distributed load.
Axial Stress
Stress calculation for axial load.
Bending Stress
Flexural stress in beams.
Shear Stress (Beam)
Shear stress in beams.
Euler Buckling Load
Critical buckling load for columns.
Cantilever Deflection (Point Load)
Max deflection at free end.
Cantilever Deflection (UDL)
Max deflection at free end.
SS Beam Deflection (Point Load Center)
Max deflection at center.
SS Beam Deflection (UDL)
Max deflection at center.
Fixed End Moment (UDL)
Fixed end moment for beam with UDL.
Fixed End Moment (Point Load)
Fixed end moment for beam with center point load.
Balanced Steel Ratio
Reinforcement ratio for balanced condition.
Nominal Moment Capacity (Singly)
Nominal moment capacity of singly reinforced beam.
Depth of Compression Block
Depth of equivalent rectangular stress block.
Slenderness Ratio
Measure of column flexibility.
Radius of Gyration
Geometric property of a cross section.
Stiffness (Axial)
Axial stiffness of a member.
Torsional Shear Stress
Shear stress due to torsion.
Polar Moment of Inertia (Circle)
Polar moment of inertia for solid circular shaft.
Thermal Stress
Stress due to restrained thermal expansion.
Axial Elongation
Change in length due to axial load.
Beta 1 Factor
Factor relating depth of equivalent rectangular stress block to neutral axis depth.
Shear Capacity of Concrete
Simplified calculation for shear strength provided by concrete.
Shear Capacity of Stirrups
Shear strength provided by shear reinforcement.
Nominal Axial Strength (Short Column)
Nominal axial strength of a reinforced concrete column at zero eccentricity.
Modulus of Rupture
Tensile strength of concrete for deflection calculations.
Modular Ratio
Ratio of modulus of elasticity of steel to concrete.
Modulus of Elasticity (Concrete)
Modulus of elasticity for normal weight concrete.
Development Length (Tension)
Basic development length equation for deformed bars in tension.
Effective Stress
The principle of effective stress, representing the stress carried by the soil skeleton.
Terzaghi's Bearing Capacity (Square Footing)
Ultimate bearing capacity for a square footing based on Terzaghi's theory.
Darcy's Law (Flow Rate)
Describes the flow of fluid through a porous medium.
Void Ratio and Porosity Relationship
Relationship between void ratio (e) and porosity (n).
Rankine Active Earth Pressure Coefficient
Calculates the active earth pressure coefficient for cohesionless soil with a horizontal surface.
Consolidation Settlement (Normally Consolidated)
Estimates the primary consolidation settlement for normally consolidated clay.
Void Ratio
Ratio of void volume to solid volume.
Porosity
Ratio of void volume to total volume.
Degree of Saturation
Percentage of voids filled with water.
Water Content
Ratio of weight of water to solids.
Unit Weight
Total weight per unit volume.
Dry Unit Weight
Unit weight of soil when dry.
Basic Soil Relation
Fundamental relationship.
Effective Stress
Total stress minus pore water pressure.
Shear Strength (Mohr-Coulomb)
Soil shear strength equation.
Active Earth Pressure Coeff
Rankine active pressure coefficient.
Passive Earth Pressure Coeff
Rankine passive pressure coefficient.
Consolidation Settlement (NC)
Settlement for normally consolidated clay.
Time Factor (Consolidation)
Dimensionless time factor.
Darcy's Law
Flow through porous media.
Hydraulic Gradient
Head loss per unit length.
Seepage Velocity
Velocity of water through voids.
Terzaghi Bearing Capacity (Strip)
Ultimate bearing capacity for strip footing.
Group Index
AASHTO classification parameter.
Relative Density
Density state of granular soil.
Flow Net Discharge
Seepage calculation from flow net.
Plasticity Index
Range of water content over which soil behaves plastically.
Liquidity Index
Scaling of natural water content relative to limits.
Activity
Plasticity index divided by percent of clay-sized particles.
Bernoulli's Equation
Conservation of energy principle for flowing fluids.
Manning's Equation
Empirical formula for estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid.
Reynolds Number
Dimensionless quantity used to predict flow patterns (laminar or turbulent).
Darcy-Weisbach Equation
Calculates the head loss due to friction in a pipe.
Hazen-Williams Equation (SI)
Empirical relationship for the flow of water in a pipe (SI units).
Hydrostatic Pressure
Pressure exerted by a fluid at equilibrium at a given depth.
Density
Mass per unit volume.
Specific Weight
Weight per unit volume.
Specific Gravity
Ratio of density to water density.
Hydrostatic Pressure
Pressure at depth h.
Hydrostatic Force (Plane)
Force on submerged plane.
Center of Pressure
Location of hydrostatic force.
Buoyancy
Archimedes principle.
Continuity Equation
Conservation of mass for incompressible flow.
Bernoulli Equation
Conservation of energy.
Torricelli's Theorem
Velocity of efflux.
Reynolds Number
Flow regime indicator.
Darcy-Weisbach Equation
Head loss due to friction.
Hazen-Williams Equation
Water flow velocity (SI).
Manning's Equation
Open channel flow velocity.
Chezy Formula
Uniform flow velocity.
Froude Number
Flow state (critical/sub/super).
Hydraulic Radius
Area divided by wetted perimeter.
Rectangular Weir Discharge
Francis formula for suppressed weir.
Triangular Weir Discharge
For 90 degree V-notch.
Pump Power
Power required by pump.
Stopping Sight Distance
Distance required for a driver to detect a hazard and bring the vehicle to a stop (Metric).
Superelevation
Relationship between superelevation, side friction, speed, and radius for horizontal curves.
Peak Hour Factor
Measure of traffic demand fluctuation within the peak hour.
Minimum Radius of Horizontal Curve
Calculates the minimum radius for a horizontal curve given design speed and maximum superelevation.
Greenshields Model
Linear relationship between speed and density in traffic flow.
Stopping Sight Distance
Distance to stop vehicle.
Superelevation
Banking of curves.
Peak Hour Factor
Traffic flow consistency.
Greenshields Model
Flow equals density times speed.
Time Mean Speed
Arithmetic mean of spot speeds.
Space Mean Speed
Harmonic mean of speeds.
Yellow Interval
Traffic signal yellow time.
Radius of Relative Stiffness
Westergaard's analysis.
Structural Number
AASHTO flexible pavement design.
ESAL
Equivalent Single Axle Loads.
Poisson Arrival
Probability of n vehicles arriving.
M/M/1 Queue Length
Average number in system.
Webster's Optimal Cycle
Signal cycle length.
Saturation Flow
Max flow rate.
Parabolic Vertical Curve
Elevation on vertical curve.
Length of Crest Curve (SSD<L)
For SSD.
Length of Sag Curve
Headlight sight distance criteria.
Degree of Curve (Arc)
Angle subtended by 20m arc.
Middle Ordinate
Distance from curve to chord.
External Distance
Distance from PI to curve.
Concrete Volume (Slab)
Calculates the volume of concrete required for a slab.
Cost Performance Index (CPI)
A measure of the cost efficiency of budgeted resources expressed as the ratio of earned value to actual cost.
Schedule Performance Index (SPI)
A measure of schedule efficiency expressed as the ratio of earned value to planned value.
Productivity Rate
Calculates the rate of production per unit of input (e.g., labor hour).
Brick Estimation
Estimates the number of bricks required for a wall of single brick thickness.
PERT Expected Time
Weighted average time.
PERT Standard Deviation
SD of activity duration.
Total Float
Slack time.
Free Float
Delay allowance without affecting successor.
Productivity
Work rate.
Volume (Trapezoidal)
Average end area method.
Volume (Prismoidal)
More accurate earthwork volume.
Swell Factor
Volume increase upon excavation.
Shrinkage Factor
Volume decrease upon compaction.
Equipment Production
Hourly production.
Cycle Time
Total time per cycle.
Number of Bricks
Estimate brick count.
Return on Investment
Profitability measure.
Factor of Safety
Capacity over Demand.
Concrete Yield
Volume of concrete produced.
Quadratic Formula
Solution for finding roots of a quadratic equation ax² + bx + c = 0.
Heron's Formula (Area of Triangle)
Calculates the area of a triangle given the lengths of its three sides.
Volume of Cylinder
Calculates the volume of a cylinder.
Pythagorean Theorem
Relates the lengths of the sides of a right triangle.
Derivative (Power Rule)
Standard formula for finding the derivative of a power function.
Compound Interest
Calculates the amount of money accumulated after n years, including interest.
Pythagorean Theorem
Right triangle sides.
Sine Law
Triangle relation.
Cosine Law
Triangle side relation.
Heron's Formula
Area of triangle.
Area of Circle
Circle area.
Circumference
Circle perimeter.
Volume of Sphere
Sphere volume.
Surface Area of Sphere
Sphere surface area.
Volume of Cone
Cone volume.
Arithmetic Series Sum
Sum of arithmetic progression.
Geometric Series Sum
Sum of geometric progression.
Power Rule (Integral)
Integral of power function.
Logarithm Rule
Log product rule.
Euler's Identity
Fundamental identity.
Taylor Series
Series expansion.
Standard Deviation
Measure of variation.
Combination
Selection without order.
Resultant of Two Forces
Calculates the magnitude of the resultant force of two concurrent forces.
Moment of a Force
Calculates the moment of a force about a point.
Centroid of a Rectangle
Location of the centroid for a rectangular area.
Moment of Inertia (Rectangle)
Moment of inertia of a rectangle about its centroidal x-axis.
Kinematics: Velocity-Time
Calculates final velocity under constant acceleration.
Kinetic Energy
Energy possessed by an object due to its motion.
Newton's Second Law
Force mass acceleration.
Weight
Force of gravity.
Friction
Friction force.
Work
Work done by force.
Potential Energy
Gravitational energy.
Power
Rate of doing work.
Momentum
Mass in motion.
Impulse
Change in momentum.
Centripetal Force
Force for circular motion.
Hooke's Law (Spring)
Spring force.
Spring Potential Energy
Energy stored in spring.
Torque
Rotational force.
Angular Velocity
Rotation rate.
Stress
Force per area.
Strain
Deformation ratio.
Young's Modulus
Stiffness.
Poisson's Ratio
Lateral strain ratio.
Shear Modulus
Modulus of rigidity.
Horizontal Distance (Slope)
Calculates the horizontal distance given the slope distance and vertical angle.
Temperature Correction (Taping)
Correction for tape length due to temperature difference.
Differential Leveling
Calculates elevation using Height of Instrument method.
Latitude and Departure
Components of a traverse line.
Area by Coordinates
Calculates the area of a polygon given the coordinates of its vertices.
Curvature and Refraction Correction
Combined correction for earth curvature and atmospheric refraction (Metric).
Horizontal Distance
Slope to horizontal.
Vertical Distance
Vertical component.
Latitude & Departure
Traverse components.
Linear Error of Closure
Traverse error.
Relative Precision
Accuracy ratio.
Temp Correction
Tape temp adjustment.
Pull Correction
Tape tension adjustment.
Sag Correction
Tape sag adjustment.
Leveling Equation
Elevation calculation.
Curvature & Refraction
Correction for long sights.
Stadia Horizontal
Stadia distance.
Stadia Vertical
Stadia elevation diff.
Compass Rule
Traverse adjustment.
Area by Coordinates
Shoelace formula.
Area by DMD
Double Meridian Distance.
Photo Scale
Photogrammetry scale.
Parallax Height
Object height from parallax.
Azimuth from Bearing
Angle from North.
Bearing from Azimuth
Quadrant direction.
Sensitivity of Bubble
Bubble tube sensitivity.
Hooke's Law
Relationship between stress and strain within the elastic limit.
Poisson's Ratio
Ratio of transverse strain to axial strain.
Shear Modulus (Modulus of Rigidity)
Relationship between Shear Modulus, Young's Modulus, and Poisson's Ratio.
Thermal Strain
Strain induced by a change in temperature.
Specific Gravity
Ratio of the weight of a given volume of material to the weight of an equal volume of water.
Water Content
Ratio of the weight of water to the weight of solids in a given volume of soil.
Density
Mass density.
Specific Gravity
Relative density.
Moisture Content
Percent moisture.
Absorption
Water absorption capacity.
Fineness Modulus
Aggregate grading.
Concrete Mean Strength
Target mix strength.
Water-Cement Ratio
Mix proportion.
Voids in Aggregate
Space between particles.
Yield Strength
Stress at which plastic deformation begins.
Ultimate Strength
Max stress.
Modulus of Elasticity
Material stiffness.
Bulk Modulus
Volumetric stiffness.
Modulus of Toughness
Energy to fracture.
Modulus of Resilience
Elastic energy capacity.
Thermal Expansion
Strain per degree temp.
Brinell Hardness
Hardness test.
Charpy Impact
Energy absorbed.
Fatigue Life
Cycles to failure.
Creep Strain
Time dependent deformation.
BOD Removal Efficiency
Percentage of Biochemical Oxygen Demand removed in a treatment process.
Hydraulic Loading Rate
Volume of wastewater applied to the surface area of a treatment unit per unit time.
Geometric Population Growth
Population projection assuming a constant percentage growth rate.
Sound Pressure Level
Logarithmic measure of the effective pressure of a sound relative to a reference value.
Stokes' Law (Settling Velocity)
Calculates the settling velocity of spherical particles in a fluid.
Food to Microorganism Ratio (F/M)
Ratio of food entering the system to the biomass in the reactor.
BOD First Order
Organic matter decay.
5-Day BOD
Standard BOD test.
Oxygen Sag Equation
Streeter-Phelps.
Stokes Law
Particle settling velocity.
Surface Loading Rate
Tank design.
Weir Loading Rate
Clarifier design.
F/M Ratio
Food to Microorganism.
Sludge Age (MCRT)
Mean cell residence time.
Chick's Law
Disinfection kinetics.
Total Hardness
As CaCO3.
Alkalinity
Buffering capacity.
Sound Level Addition
Decibel addition.
Sound Distance Attenuation
Point source decay.
Gaussian Plume
Air pollution concentration.
Landfill Volume
Space required.
Rational Method
Stormwater runoff.
Darcy Flux
Groundwater flow.
Retardation Factor
Contaminant transport.
Half Life
Time to half decay.
Carcinogenic Risk
Health risk.
Simple Interest
Calculates the interest amount based on principal, time, and rate.
Compound Amount (Single Payment)
Calculates the future worth of a present amount.
Sinking Fund Factor
Calculates the uniform series amount required to accumulate a future sum.
Capital Recovery Factor
Calculates the uniform series amount equivalent to a present sum.
Benefit-Cost Ratio
Ratio of the present value of benefits to the present value of costs.
Break-Even Analysis
Determines the quantity at which total revenue equals total cost.
Present Worth (P/F)
Discounting.
Uniform Series PW (P/A)
Present value of annuity.
Uniform Series FW (F/A)
Future value of annuity.
Gradient PW (P/G)
Arithmetic gradient.
Effective Interest Rate
Annual effective rate.
Rule of 72
Doubling time.
Straight Line Depreciation
Uniform depreciation.
Sum of Years Digits
Accelerated depreciation.
Declining Balance
Fast write-off.
Bond Value
Price of bond.
Capitalized Cost
Perpetual cost.
Benefit Cost Ratio
Project feasibility.
Perpetuity
Infinite annuity.
Inflation Adjusted Rate
Real interest rate.
Payback Period
Simple return time.
Rational Method (Peak Runoff)
Estimates the peak discharge from a small watershed.
SCS Curve Number Method (Runoff Depth)
Estimates direct runoff depth from rainfall depth.
Horton's Infiltration Equation
Describes the infiltration capacity of soil over time.
Specific Yield
Ratio of the volume of water a rock or soil will yield by gravity drainage to the total volume.
Darcy's Law (Groundwater Flow)
Describes the flow of fluid through a porous medium.
Muskingum Method (Outflow)
Calculates the outflow at the end of a time step for flood routing.
Water Balance
Mass balance.
Runoff Coefficient
Ratio of runoff to rainfall.
Phi Index
Infiltration index.
Muskingum Method
Flood routing.
Thiem Eq (Confined)
Well flow confined.
Dupuit Eq (Unconfined)
Well flow unconfined.
Transmissivity
Aquifer property.
Storativity
Storage coeff.
Specific Capacity
Well productivity.
Penman Equation
Evapotranspiration.
SCS Curve Number
Runoff estimation.
Potential Retention
Max retention.
Hyetograph Intensity
Rainfall intensity.
Return Period
Recurrence interval.
Hydrologic Risk
Prob of event in n years.
Reservoir Capacity (Ripple)
Mass curve analysis.
Gumbel Distribution
Extreme value stats.
Weber Number
Surface tension forces.
Mach Number
Compressibility.
Bulk Modulus (Fluid)
Fluid elasticity.
Coulomb's Law
Electric force between two charges.
Ohm's Law
Relationship between voltage, current, and resistance.
Ideal Gas Law
Equation of state for an ideal gas.