Think it. Compute it. Ship it.

Yes. Every engineering calculator, design studio, reference library, and analysis tool on Phaxor is completely free. There is no sign-up, no subscription, no trial period, and no credit card required. Open any tool and start calculating immediately. The API and Python library are also free for personal and educational use.

Phaxor covers seven major engineering disciplines with over 100 calculators: Structural (stress-strain analysis, Mohr's circle, failure theories, beam deflection, column buckling, RCC beam/slab/column design, isolated footing, bearing capacity, earth pressure, soil properties, settlement, development length, reinforcement quantity); Mechanical (torque and power, gear ratio, belt drive, pressure and force, SFD/BMD beam analysis, shaft design, spring design, bearing life, bolt analysis, weld strength, flywheel design, vibration analysis, heat transfer, heat exchanger, Rankine cycle, ideal gas law, COP, pipe flow, pump power, tolerance analysis); Electrical (Ohm's law, AC power, energy consumption, power factor correction, impedance, resonance, efficiency, transformer, induction motor, DC motor, cable sizing, circuit breaker, earthing, battery and UPS sizing, short circuit analysis, solar PV sizing, rectifier); Chemical (stoichiometry, Arrhenius kinetics, CSTR design, PFR design, chemical equilibrium, vapor-liquid equilibrium, distillation column, packed bed pressure drop, Gibbs free energy); Hydraulics & Transport (open channel flow, weir and orifice, sight distance, pavement thickness); Materials (hardness conversion, fatigue life, corrosion rate, rule of mixtures, atomic packing factor); plus 15 interactive design studios and reference libraries.

Engineering Studios are advanced interactive workspaces for multi-step design and analysis tasks that go beyond single-formula calculators. They include: Failure Checker (multi-criterion failure analysis using von Mises, Tresca, Maximum Normal Stress, Coulomb-Mohr, and Modified Mohr theories); Material Finder (search and filter engineering materials by yield strength, tensile strength, elastic modulus, density, Poisson's ratio); Parametric Optimizer (automated design-space sweeps to find optimal configurations minimizing weight, cost, or stress under constraints); Monte Carlo Simulator (probabilistic analysis with thousands of randomized simulations producing statistical distributions); Cost Calculator (estimate material and fabrication costs); Flow Studio (fluid dynamics analysis); Forces Studio (static equilibrium and load path analysis); Thermal Profiler (temperature distribution and heat flow); Materials Studio, Chemical Studio, Ceramic Studio, Magnet Studio, Plastic & PVC Studio, and Semiconductor Studio (domain-specific property analysis and design workspaces).

The Failure Checker Studio performs multi-criterion failure analysis on a given stress state. Enter your principal stresses (σ₁, σ₂, σ₃) and material properties (yield strength Sᵧ, ultimate tensile strength Sᵤᵗ, ultimate compressive strength Sᵤᶜ), and it simultaneously evaluates: von Mises (distortion energy) criterion, Tresca (maximum shear stress) criterion, Maximum Normal Stress theory, Coulomb-Mohr theory for brittle materials, and Modified Mohr theory. Each criterion reports whether the design is safe or failed, with the safety factor and graphical failure envelope comparisons.

The Monte Carlo Simulator runs thousands of randomized simulations to quantify uncertainty and reliability in engineering calculations. Define input parameter distributions (normal, uniform, triangular, or log-normal) with their mean and standard deviation, and the simulator produces statistical distributions of output variables — including mean value, standard deviation, coefficient of variation, 95% and 99% confidence intervals, minimum, maximum, and probability of failure (probability that the output exceeds a specified limit). Essential for reliability engineering, risk analysis, and manufacturing tolerance stackup studies.

Mohr's Circle is a graphical method for determining principal stresses and maximum shear stress from a 2D stress state. Enter the normal stresses σₓ and σᵧ and the shear stress τₓᵧ, and the calculator computes: principal stresses (σ₁, σ₂), maximum in-plane shear stress (τₘₐₓ), orientation angle (θₚ) of the principal planes, and the average normal stress. The interactive Mohr's Circle diagram is drawn with all transformation points marked for any rotation angle.

The Beam Deflection calculator computes deflection (δ), slope (θ), shear force (V), and bending moment (M) along a beam's length. It supports simply supported, cantilever, fixed-fixed, and propped cantilever beams under point loads, uniformly distributed loads (UDL), uniformly varying loads (UVL), and applied moments. Enter beam length (L), material elastic modulus (E), second moment of area (I), and loading conditions to get instant deflection curves, SFD (Shear Force Diagram), and BMD (Bending Moment Diagram) with critical values highlighted.

The Column Buckling calculator determines the critical buckling load (P⃬ℛ) for slender structural columns using Euler's formula: P⃬ℛ = π²EI / (KL)², where E is elastic modulus, I is the minimum second moment of area, K is the effective length factor for end conditions (fixed-fixed K=0.5, fixed-pinned K=0.7, pinned-pinned K=1.0, fixed-free K=2.0), and L is column length. It also calculates slenderness ratio (KL/r), radius of gyration (r), and compares critical stress against the material's yield strength to determine whether failure is by buckling or yielding.

CSTR (Continuously Stirred Tank Reactor) and PFR (Plug Flow Reactor) are the two ideal reactor models in chemical reaction engineering. A CSTR assumes perfect mixing — the composition inside the reactor is uniform and equal to the exit stream. A PFR assumes no axial mixing — reactants flow through a tube where concentration changes progressively along the length. Phaxor's design tools calculate the required reactor volume from rate law expressions (zero, first, or second order), rate constant (k), feed concentration (C₀), volumetric flow rate (v₀), and desired fractional conversion (X). Based on the design equations from Fogler and Levenspiel.

VLE describes the thermodynamic conditions under which vapor and liquid phases coexist at equilibrium. Phaxor's VLE calculator uses Raoult's Law (Pᵢ = xᵢ · γᵢ · Pᵢˢᴀᵗ) with activity coefficient models to compute bubble-point temperature, dew-point temperature, and x-y equilibrium diagrams for binary mixtures. These calculations are essential for distillation column design, determining the number of theoretical stages, minimum reflux ratio, and separation feasibility in chemical process engineering.

Impedance (Z) is the total opposition to alternating current (AC) flow, combining resistance (R in ohms) and reactance (X in ohms) as a complex number: Z = R + jX. The calculator handles series and parallel RLC circuits, computing impedance magnitude |Z| = √(R² + X²), phase angle φ = arctan(X/R), inductive reactance Xₗ = 2πfL, capacitive reactance X⁾ = 1/(2πfC), resonant frequency f₀ = 1/(2π√LC), bandwidth, and quality factor Q. Enter resistance, inductance (L), capacitance (C), and operating frequency (f) for complete AC circuit analysis.

Bearing capacity is the maximum pressure a soil foundation can support without undergoing shear failure. Phaxor's calculator uses Terzaghi's equation: qᵤ₤ᵗ = cNᶜ + qNᶢ + 0.5γBNᵦ, where c is soil cohesion, q is overburden pressure (γ × Dᵦ), γ is unit weight, B is foundation width, and Nᶜ, Nᶢ, Nᵦ are bearing capacity factors dependent on the friction angle (φ). Also implements Meyerhof's general equation with shape, depth, and inclination correction factors. Enter soil parameters and foundation geometry to determine ultimate and allowable bearing capacity with your chosen factor of safety.

Yes. All engineering tools support both SI (metric) and Imperial/US customary unit systems. Toggle the system globally with one click and all inputs, outputs, labels, and chart axes convert automatically. Supported units include meters/feet, Pascals/psi/ksi, Newtons/pounds-force, kilograms/pounds-mass, Celsius/Fahrenheit/Kelvin, Joules/BTU, Watts/horsepower, cubic meters/cubic yards, millimeters/inches, kN/kips, MPa/ksi, and many more. Units are clearly labeled on every input and output field.

Yes. Phaxor is fully responsive and works on smartphones, tablets, laptops, and desktops. All tools, interactive charts, and design studios are optimized for touch interfaces and small screens. The layout adapts to any screen width, and all controls remain accessible.

Yes. Phaxor provides a REST API for programmatic access to all engineering calculations — send JSON requests with your inputs and receive computed results. There is also an open-source Python library (pip install phaxor) for use in scripts, Jupyter notebooks, automation pipelines, and integration with other engineering software. Visit the API Documentation and Python Library pages for endpoints, authentication details, rate limits, and usage examples.

All formulas are implemented from verified engineering references, textbooks, and design codes — including Euler-Bernoulli beam theory, Timoshenko beam theory, Mohr's circle stress transformations, Terzaghi and Meyerhof bearing capacity equations, Darcy-Weisbach pipe flow equation, Manning's equation for open channels, Clausius-Clapeyron and Antoine equation for phase equilibria, Fogler/Levenspiel reactor design equations, and standard motor/transformer equivalent circuits. Results are cross-validated against industry-standard software. However, all tools are for educational and preliminary design use — always verify critical or safety-sensitive calculations with a licensed professional engineer.

The Rankine Cycle calculator analyzes the ideal and actual thermodynamic cycle used in steam power plants. It computes thermal efficiency (ηᵗᵈ = Wₙᵉᵗ/Qᵢₙ), net work output, heat input, and heat rejection across four stages: isobaric heating in the boiler, isentropic expansion in the turbine, isobaric cooling in the condenser, and isentropic compression in the pump. You can specify isentropic efficiencies for the turbine and pump to compare ideal versus actual cycle performance. Enter boiler pressure, condenser pressure, and superheat temperature to get complete cycle analysis with T-s diagram.

Gibbs Free Energy (G) determines the spontaneity of a chemical reaction at constant temperature and pressure using ΔG = ΔH − TΔS, where ΔH is enthalpy change, T is absolute temperature (Kelvin), and ΔS is entropy change. If ΔG < 0, the reaction is spontaneous (exergonic). If ΔG > 0, it is non-spontaneous (endergonic). The calculator also computes the equilibrium constant K from ΔG = −RT ln(K), and determines the temperature at which a reaction becomes spontaneous.

The Tolerance Analysis Studio performs statistical and worst-case tolerance stackup analysis for mechanical assemblies. Define the dimensional chain of parts with their nominal dimensions and bilateral tolerances, and the studio calculates the resulting assembly variation using both worst-case (arithmetic stackup: Δᵗᵤ = Σ|Δᵢ|) and statistical (Root Sum Square: Δₛₛₛ = √ΣΔᵢ²) methods. It reports assembly nominal dimension, maximum and minimum assembly sizes, and the probability that parts will fit within specification. Essential for ensuring manufactured parts assemble correctly within production variability.

SFD (Shear Force Diagram) and BMD (Bending Moment Diagram) are graphical representations of the internal shear force (V) and bending moment (M) along a beam's length for given support and loading conditions. The Beam SFD/BMD calculator supports any combination of simple supports, cantilever, and fixed supports with point loads, distributed loads, and applied moments. It plots the complete SFD and BMD, identifies critical values (maximum shear, maximum moment), locates inflection points and zero-crossing locations, and reports support reactions. These diagrams are fundamental to structural and mechanical beam design.

The Arrhenius Equation calculator computes the temperature dependence of reaction rate constants using k = A · exp(−Eᴀ/RT), where A is the pre-exponential (frequency) factor, Eᴀ is the activation energy (J/mol or kJ/mol), R is the universal gas constant (8.314 J/mol·K), and T is absolute temperature (Kelvin). Enter any two known rate-temperature data points to determine the activation energy, or specify Eᴀ and A to compute k at any temperature. Used extensively in chemical kinetics, catalysis, polymer degradation, and food science.