Our Methodology

Accurate calculations built on established engineering standards

Data Sources

Our calculators are built using data from authoritative sources in the engineering and manufacturing industry:

Primary References

  • Machinery's Handbook (31st Ed.) - Mechanical engineering data
  • ASME Standards - Mechanical specifications
  • ASTM Standards - Material testing (E140 hardness, etc.)
  • ISO Standards - International metric specifications

Industry Standards

  • AWS D1.1 - Structural Welding Code
  • NEC - National Electrical Code
  • AISC - Steel Construction Manual
  • NEMA MG-1 - Motors and Generators

Calculation Principles

Each calculator follows these design principles:

Conservative Defaults

When ranges exist, we default to safer values. 75% thread engagement, not 100%. 80% rated capacity, not peak.

Transparent Formulas

Every formula is documented below. No black boxes—verify our math against your references.

Industry-Standard Units

Full support for Imperial and Metric with NIST-traceable conversion factors.

Practical Validation

Inputs are checked against realistic ranges. Out-of-bounds values produce warnings.

Precision & Rounding

Output Type Precision Rationale
RPM, Feed Rates Whole numbers Machine controls don't accept decimals
Dimensions (in) 4 decimal places Standard machining tolerance precision
Dimensions (mm) 2 decimal places 0.01mm precision standard
Torque, Force 1-2 decimal places Practical measurement accuracy
Percentages 1 decimal place Sufficient for engineering use
Weight 2 decimal places Scale accuracy in shop environment

Internal calculations use full floating-point precision. Rounding is applied only to displayed output.

Unit Conversions

Key conversion factors used throughout (per NIST SP 811):

Length

  • 1 inch = 25.4 mm (exact)
  • 1 foot = 0.3048 m (exact)
  • 1 mm = 0.03937 in

Force & Torque

  • 1 lbf = 4.44822 N
  • 1 lb-ft = 1.35582 Nm
  • 1 lb-in = 0.112985 Nm

Pressure

  • 1 psi = 6.89476 kPa
  • 1 bar = 14.5038 psi
  • 1 MPa = 145.038 psi

Power

  • 1 HP = 0.7457 kW
  • 1 HP = 550 ft-lb/s
  • 1 kW = 1.341 HP

Calculator Formulas & Standards

CNC Speed & Feed Calculator

Formulas

Spindle Speed (RPM): RPM = (SFM × 12) ÷ (π × D)

Where SFM = Surface Feet per Minute, D = cutter diameter in inches

Feed Rate (IPM): IPM = RPM × FPT × Z

Where FPT = Feed Per Tooth, Z = number of flutes

Metric Version: RPM = (Vc × 1000) ÷ (π × D)

Where Vc = cutting speed in m/min, D = diameter in mm

Standards & References

  • Machinery's Handbook 31st Ed., Ch. 23
  • ISO 3685:1993 Tool Life Testing

Assumptions

  • Rigid setup with minimal vibration
  • Sharp, uncoated carbide tooling as baseline
  • Dry cutting conditions (adjust for coolant)
Open Calculator
Hardness Converter

Formulas

Conversion Tables: Empirical conversion tables

Non-linear relationships derived from experimental data

Standards & References

  • ASTM E140-12b Standard Hardness Conversion Tables
  • ISO 18265:2013 Metallic Materials Hardness Conversion

Assumptions

  • Homogeneous material
  • Standard test conditions per ASTM E18 (Rockwell), E10 (Brinell)
  • Conversions are approximate—direct testing preferred for critical applications
Open Calculator
Sheet Metal Bend Calculator

Formulas

Bend Allowance: BA = A × (π/180) × (R + K × T)

Where A = bend angle, R = inside radius, K = K-factor, T = thickness

Bend Deduction: BD = 2 × (R + T) × tan(A/2) - BA

Amount to subtract from flat length

K-Factor: K = t/T

Where t = distance to neutral axis, T = material thickness

Standards & References

  • Machinery's Handbook, Sheet Metal section
  • ASME Y14.5 for dimensioning

Assumptions

  • K-factor of 0.33 for soft materials, 0.50 for hard materials as defaults
  • Air bending (not bottoming or coining)
  • Uniform material thickness
Open Calculator
Hydraulic Force Calculator

Formulas

Cylinder Force: F = P × A

Where F = force (lbs or N), P = pressure (psi or Pa), A = piston area

Piston Area: A = π × (D/2)²

Where D = bore diameter

Retract Force: F = P × (A_bore - A_rod)

Accounts for rod cross-section on retract stroke

Standards & References

  • ISO 6020/6022 Hydraulic Cylinders
  • NFPA T3.6.7 Cylinder Dimensions

Assumptions

  • Incompressible fluid
  • No friction losses (actual force ~95% of theoretical)
  • Atmospheric back-pressure
Open Calculator
Weld Consumables Estimator

Formulas

Filler Weight: W = V × ρ × (1 + loss%)

Where V = weld volume, ρ = filler density, loss% accounts for spatter

Weld Volume (Fillet): V = 0.5 × L² × length

Where L = leg size

Weld Volume (Groove): V = A × length

Where A = groove cross-sectional area

Standards & References

  • AWS A5.1 (SMAW)
  • AWS A5.18 (GMAW)
  • AWS A5.20 (FCAW)

Assumptions

  • Deposition efficiency: SMAW 65%, GMAW 95%, FCAW 85%
  • Spatter loss included in efficiency
  • Single-pass or calculated multi-pass
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Bolt Torque Calculator

Formulas

Torque-Tension: T = K × D × F

Where T = torque, K = nut factor, D = nominal diameter, F = clamp load

Clamp Load: F = 0.75 × At × Sp

Where At = tensile stress area, Sp = proof strength

Standards & References

  • SAE J429 (Grade 5, 8)
  • ISO 898-1 (Class 8.8, 10.9, 12.9)
  • Machinery's Handbook Fastener section

Assumptions

  • K = 0.20 for dry steel, 0.15 for lubricated
  • 75% of proof load as default (industry standard)
  • New, undamaged threads
Open Calculator
Drill & Tap Chart

Formulas

Tap Drill (Imperial): TD = D - (1/TPI × %thread)

Where D = major diameter, TPI = threads per inch

Tap Drill (Metric): TD = D - (P × %thread)

Where P = pitch in mm

Thread Percentage: % = (D - TD) / (1/TPI) × 100

Actual thread engagement percentage

Standards & References

  • ANSI/ASME B1.1 Unified Threads
  • ISO 68-1 Metric Threads
  • ASME B94.11M Twist Drills

Assumptions

  • 75% thread engagement as default
  • Standard tap drill sizes (not exact calculated)
  • Class 2B/6H fit
Open Calculator
Material Weight Calculator

Formulas

Weight: W = V × ρ

Where V = volume, ρ = material density

Round Bar Volume: V = π × (D/2)² × L

Diameter and length

Rectangular Volume: V = W × H × L

Width, height, length

Tube Volume: V = π × L × (OD² - ID²) / 4

Outer diameter, inner diameter, length

Standards & References

  • ASTM material specifications for density values
  • AISI/SAE material designations

Assumptions

  • Nominal density values (actual varies by alloy/heat)
  • Room temperature properties
  • No mill tolerances applied
Open Calculator
Torque & Power Converter

Formulas

Power from Torque: HP = (T × RPM) / 5252

Where T = torque in lb-ft

Metric Power: kW = (T × RPM) / 9549

Where T = torque in Nm

HP to kW: kW = HP × 0.7457

Exact conversion factor

Standards & References

  • NIST SP 811 Guide for SI Units
  • IEEE/ASTM SI 10

Assumptions

  • Mechanical horsepower (550 ft-lb/s)
  • No efficiency losses in conversion
Open Calculator
Electrical Wire Sizing Calculator

Formulas

Voltage Drop: Vd = (2 × L × I × R) / 1000

Where L = length in ft, I = current, R = resistance per 1000ft

Circular Mils: CM = (2 × K × I × L) / Vd

Where K = resistivity constant (copper = 12.9)

Standards & References

  • NEC Article 310 Conductor Ampacity
  • NEC Chapter 9 Table 8 DC Resistance
  • IEEE 141 (Red Book)

Assumptions

  • Copper conductor at 75°C rating
  • 3% voltage drop maximum for branch circuits
  • Single-phase calculation (3-phase uses 1.732 factor)
Open Calculator
Thread Pitch Calculator

Formulas

Pitch (Metric): P = 1 / TPI × 25.4

Convert TPI to mm pitch

Minor Diameter: d = D - 1.0825 × P

For 60° thread form

Pitch Diameter: d2 = D - 0.6495 × P

Theoretical pitch diameter

Standards & References

  • ASME B1.1 Unified Inch Threads
  • ISO 68-1 / ISO 261 Metric Threads

Assumptions

  • 60° thread angle (UN/ISO)
  • Basic thread profile
  • External thread dimensions
Open Calculator
Surface Finish Converter

Formulas

Ra to RMS: RMS ≈ Ra × 1.11

Approximate conversion for typical surfaces

Ra to Rz: Rz ≈ Ra × 4 to 7

Depends on machining process (milling ~4, grinding ~6)

CLA to Ra: Ra = CLA

Center Line Average = Arithmetic Average (Ra)

Standards & References

  • ISO 4287:1997 Surface Texture Parameters
  • ASME B46.1 Surface Texture
  • ISO 1302 Surface Texture Indication

Assumptions

  • Conversions are approximate (surface-dependent)
  • Gaussian amplitude distribution assumed
  • Standard cutoff wavelength (0.8mm typical)
Open Calculator
Spring Calculator

Formulas

Spring Rate: k = (G × d⁴) / (8 × D³ × Na)

Where G = shear modulus, d = wire dia, D = mean coil dia, Na = active coils

Force: F = k × δ

Where δ = deflection

Stress: τ = (8 × F × D × Kw) / (π × d³)

Where Kw = Wahl correction factor

Standards & References

  • SMI Handbook of Spring Design
  • Associated Spring Design Handbook

Assumptions

  • Music wire or chrome silicon as default material
  • Static loading (no fatigue)
  • Ground and squared ends
Open Calculator
Beam Load Calculator

Formulas

Simple Beam Deflection (Center Load): δ = (P × L³) / (48 × E × I)

Where P = load, L = span, E = modulus, I = moment of inertia

Bending Stress: σ = (M × c) / I

Where M = moment, c = distance to neutral axis

Maximum Moment (Center): M = P × L / 4

For simply supported beam with center point load

Standards & References

  • AISC Steel Construction Manual
  • ASCE 7 Minimum Design Loads
  • Machinery's Handbook Beam Formulas

Assumptions

  • Linear elastic behavior
  • Small deflections (< L/300)
  • Simply supported end conditions
  • Homogeneous, isotropic material
Open Calculator
Pneumatic Cylinder Sizing

Formulas

Theoretical Force: F = P × A × η

Where η = efficiency factor (~0.85)

Bore from Force: D = √(4 × F / (π × P × η))

Solve for required bore diameter

Air Consumption: Q = A × S × n × (P + 14.7) / 14.7

SCFM based on stroke, speed, pressure

Standards & References

  • ISO 15552 Pneumatic Cylinders
  • ISO 6432 Mini Cylinders
  • NFPA T3.9.5

Assumptions

  • 85% mechanical efficiency
  • Dry air at standard conditions
  • No significant back-pressure
Open Calculator
Gear Ratio Calculator

Formulas

Gear Ratio: GR = N_driven / N_driver

Where N = number of teeth

Output RPM: RPM_out = RPM_in / GR

Speed reduction

Output Torque: T_out = T_in × GR × η

Where η = efficiency (~98% per mesh)

Standards & References

  • AGMA 2001-D04 Gear Rating
  • ISO 21771 Gear Geometry

Assumptions

  • 98% efficiency per gear mesh
  • Spur or helical gears
  • No backlash consideration
Open Calculator
Thermal Expansion Calculator

Formulas

Linear Expansion: ΔL = α × L₀ × ΔT

Where α = coefficient of thermal expansion

Final Length: L = L₀ × (1 + α × ΔT)

Original length plus expansion

Volumetric: ΔV ≈ 3α × V₀ × ΔT

Approximate for isotropic materials

Standards & References

  • ASTM E228 Linear Thermal Expansion
  • CRC Handbook of Chemistry and Physics

Assumptions

  • Constant CTE over temperature range (linear approximation)
  • Unconstrained expansion
  • Isotropic material
Open Calculator
Belt & Pulley Calculator

Formulas

Speed Ratio: n₂/n₁ = D₁/D₂

Where n = RPM, D = pitch diameter

Belt Length: L = 2C + π(D₁+D₂)/2 + (D₂-D₁)²/(4C)

Where C = center distance

Belt Speed: V = π × D × n / 12

Feet per minute

Standards & References

  • RMA (Rubber Manufacturers Association) Standards
  • ISO 5292 Belt Drives

Assumptions

  • No belt slip (2-5% actual)
  • Proper belt tension
  • V-belt or synchronous belt
Open Calculator
Air Compressor Sizing

Formulas

Total CFM: CFM_total = Σ(CFM × duty%)

Sum of all tool CFM requirements × duty cycle

With Safety Factor: CFM_required = CFM_total × 1.25

25% safety margin recommended

Tank Size: V = (CFM × P_cut-in) / (P_cut-out - P_cut-in)

Minimum tank for cycle time

Standards & References

  • CAGI (Compressed Air & Gas Institute) Standards
  • ISO 1217 Compressor Testing

Assumptions

  • Duty cycle based on typical usage patterns
  • 25% safety factor for peak demand
  • Standard pressure (90-125 psi)
Open Calculator
Motor Sizing Calculator

Formulas

HP from Torque: HP = (T × n) / 5252

Where T = torque (lb-ft), n = RPM

kW from Torque: kW = (T × n) / 9549

Where T = torque (Nm)

With Service Factor: HP_nameplate = HP_required / SF

Typical SF = 1.15 for general purpose

Standards & References

  • NEMA MG-1 Motors and Generators
  • IEC 60034 Rotating Machines
  • IEEE 112 Motor Efficiency Testing

Assumptions

  • Continuous duty (S1)
  • Standard NEMA frame efficiency
  • 1.15 service factor for TEFC motors
Open Calculator
Weld Heat Input Calculator

Formulas

Heat Input: HI = (V × A × 60) / (S × 1000)

kJ/mm, where V = volts, A = amps, S = travel speed (mm/min)

Imperial Version: HI = (V × A × 60) / (S × 1000)

kJ/in, where S = travel speed (in/min)

With Efficiency: HI_net = HI × η

η varies by process: GTAW 0.6, GMAW 0.8, SMAW 0.8, SAW 0.95

Standards & References

  • AWS D1.1 Structural Welding Code - Steel
  • ASME Section IX Welding Qualifications
  • EN 1011-1 Welding Recommendations

Assumptions

  • Arc efficiency varies by process
  • Steady-state welding conditions
  • No preheat effect included in basic calculation
Open Calculator

Material Data

Material properties (density, machinability, hardness ranges, thermal coefficients) are sourced from:

  • ASM Handbook series (Vols. 1, 2, 4)
  • MatWeb material property database
  • Mill certifications and specifications
  • Manufacturer technical data sheets
  • CRC Handbook of Chemistry and Physics

Note: Material properties can vary ±5-10% between suppliers, heat lots, and processing conditions. For critical applications, always verify with your material supplier's certification (MTR).

Limitations & Disclaimers

Important Notice

ShopMath calculators are tools for estimation and reference. They are not substitutes for professional engineering judgment. Results should be verified against manufacturer specifications and adjusted for your specific conditions. For safety-critical applications, consult a licensed professional engineer.

Factors that may affect real-world results:

  • Machine rigidity and condition
  • Tool runout and wear
  • Workholding setup and clamping
  • Coolant type and application
  • Actual vs. nominal material composition
  • Environmental conditions (temp, humidity)
  • Operator technique and experience
  • Equipment calibration status

Updates & Corrections

We continuously review and update our calculators based on user feedback, new standards revisions, and improved data sources.

If you notice an error, have a suggestion, or can provide better reference data, please contact us. We take accuracy seriously and will investigate all reported issues.

Last methodology review: January 2026