# ContainerMath

> ContainerMath is 3D container loading and cargo optimization software. It turns a cargo list (cartons, pallets, crates) into an optimized, exportable 3D load plan — computing how many items fit, their placement and loading order, CBM (volume), weight, payload and per-axle compliance across 50+ container, truck, rail and air vessel types. It pairs two linked tools: Carton Fit (how many retail units fit in a shipper carton) and Freight (how cartons and pallets load into containers). A free, no-signup CBM calculator is public; full 3D planning is on a free trial (no card) and paid plans from $39.99/mo.

## Product documentation

- [ContainerMath Documentation](https://containermath.com/guide): The complete product reference — the Freight and Carton Fit calculators, 3D load plans, weight & axle compliance, the equipment Optimizer, saved libraries (boxes, items, pallets, vessels), Stowy AI assistant, plans/pricing tiers and the developer API, with screenshots and an FAQ.

## Free tools

- [Cargo Load Planner](https://containermath.com/cargo-load-planner): Free, no-signup cargo load planner for containers, trucks, trailers and railcars. Enter one pallet or carton size, weight and quantity; it returns the floor layout (mixed orientations), how many layers stack, whether space or payload is the binding limit, and how many loads the quantity needs.
- [CBM Calculator](https://containermath.com/cbm-calculator): Free, no-signup calculator for cubic metres (CBM), cubic feet (CFT), cargo weight and container-volume utilisation across 20ft, 40ft and 40ft High Cube.
- [Container Dimensions Reference](https://containermath.com/container-dimensions): Internal/external dimensions, volume and payload for every container, trailer and rail-wagon type.

## Use inside an AI assistant (MCP)

ContainerMath is reachable over the Model Context Protocol, so an assistant can compute cargo
volume, cargo load plans, pallet counts and vessel dimensions directly in a conversation. All four tools are free,
need no key and no signup.

- MCP endpoint: `https://mcp.containermath.com` (remote, Streamable HTTP, no authentication).
- Tool `calculate_cbm`: given a list of items (length, width, height, weight, quantity in metric or
  imperial), returns total CBM/CFT, total weight, and how the cargo fills a 20ft / 40ft / 40ft High
  Cube container. Volume math only — the same calculation as the free CBM Calculator above.
- Tool `plan_cargo_load`: given a vessel (slug or plain name) and ONE cargo size (length, width,
  height, optional weight, quantity, stackable, this-side-up; metric or imperial), returns units per
  floor layer with mixed orientations, layers by interior height, units per load, whether space or
  payload binds, how many loads the quantity needs, utilisation, and a link to the same plan drawn on
  the free Cargo Load Planner page. Exact floor counts for standard pallet sizes; for other sizes the
  count is a best-block-pattern lower bound and says so.
- Tool `how_many_pallets_fit`: given a vessel (slug or plain name such as "40HC" or "53ft trailer"),
  returns how many Euro (1200×800), standard (1200×1000) and US GMA (48×40in) pallets fit — the
  solved single-layer floor count with pallets in mixed orientations, not length ÷ length, so a 20ft
  returns 11 and a 40ft returns 25 — plus the double-stacked count with the load height it requires,
  and how many the payload allows at a given gross weight per pallet.
- Tool `get_container_dimensions`: interior length/width/height, volume, floor area and maximum
  payload for all 47 containers, trailers, rail wagons and air ULDs; call it with no arguments to
  list the catalog with each vessel's slug.
- Add it in Claude Code with `claude mcp add --transport http containermath https://mcp.containermath.com`,
  or as a custom connector in claude.ai, Claude Desktop or ChatGPT.
- Listed in the official MCP Registry as `com.containermath/cbm`.
- The full 3D load plan (placement, weight & axle) is on the authenticated REST API — see Developer API below.

## Guides

- [How Many Pallets Fit in a 40ft Container?](https://containermath.com/blog/how-many-pallets-fit-in-a-40ft-container): About 25 Euro or 20–21 standard pallets single-layer (up to ~50 double-stacked) — the math, dimensions and weight limits.
- [How Many Pallets Fit in a 20ft Container?](https://containermath.com/blog/how-many-pallets-fit-in-a-20ft-container): About 11 Euro or 9–10 standard pallets single-layer, and why a 20ft suits heavy, dense cargo.
- [How Many Boxes Fit in a Container?](https://containermath.com/blog/how-many-boxes-fit-in-a-container): The volume-÷-box formula, a size-by-size table, and the weight limit most people miss.
- [How to Calculate CBM for Shipping](https://containermath.com/blog/how-to-calculate-cbm-for-shipping): CBM = length × width × height in metres; worked examples, unit conversions, and chargeable weight.
- [Shipping Container Dimensions](https://containermath.com/blog/shipping-container-dimensions): Internal, external and door dimensions plus volume for 20ft, 40ft, 40ft High Cube and 45ft.
- [Container Weight Limits & Max Payload](https://containermath.com/blog/container-weight-limits-max-payload): Max gross vs tare vs payload vs VGM, and why you rarely get to load the full payload.
- [Truck Axle Weight Limits](https://containermath.com/blog/truck-axle-weight-limits): Gross vs per-axle limits, the Federal Bridge Formula, and why distribution matters as much as total weight.
- [How to Make a Container Loading Plan](https://containermath.com/blog/how-to-make-a-container-loading-plan): The four inputs and the steps to a placement plan with a loading sequence.
- [Container Load Optimization: Maximize Space](https://containermath.com/blog/container-load-optimization-maximize-space): Moving real utilisation from a hand-planned ~75–80% toward ~90%+.
- [How to Reduce Container Shipping Costs](https://containermath.com/blog/reduce-container-shipping-costs): Seven levers, all rooted in filling each container properly.
- [LCL vs FCL: When to Switch](https://containermath.com/blog/lcl-vs-fcl-when-to-switch): The ~13–15 CBM crossover where a full container beats per-CBM LCL.
- [Best Container Loading Software in 2026](https://containermath.com/blog/best-container-loading-software): Honest comparison of ContainerMath vs EasyCargo, Cargo-Planner and CubeMaster — features, weight handling, import, API and pricing.
- [Container Loading Software: Buyer's Guide](https://containermath.com/blog/container-loading-software-buyers-guide): The 8 capabilities that separate a real load planner from a volume estimator.
- [Container Loading Software Pricing in 2026](https://containermath.com/blog/container-loading-software-pricing): Real prices for ContainerMath, EasyCargo, Cargo-Planner, Cube-IQ and CubeMaster — and why the pricing model (per seat, flat, day tickets, quote-only) matters more than the sticker.
- [How Many Pallets Fit in a 53ft Trailer?](https://containermath.com/blog/how-many-pallets-fit-in-a-53ft-trailer): 26 standard pallets floor-loaded (13 per side), up to 52 double-stacked — and why axle weight, not floor space, usually binds first.
- [Reefer Container Dimensions & Loading](https://containermath.com/blog/reefer-container-dimensions-and-loading): Real internal dimensions and payloads for 20ft/40ft reefers, plus the T-floor and red-load-line rules that govern refrigerated stows.
- [Dimensional Weight vs Actual Weight](https://containermath.com/blog/dimensional-weight-vs-cbm-chargeable-weight): How chargeable weight works — the 1:6,000 air and 1:5,000 courier divisors, worked examples, and how to stop shipping air.
- [Container Weight Distribution & Center of Gravity](https://containermath.com/blog/container-weight-distribution-and-center-of-gravity): Why a load under its weight limit can still be illegal or unsafe, and how to balance front-to-back, side-to-side and CoG height.
- [Dangerous Goods Container Segregation](https://containermath.com/blog/dangerous-goods-container-loading-segregation): The IMDG segregation levels, why incompatible classes can't share a container, and how to plan keep-apart groups in.
- [AI Container Load Planning & Smart Input](https://containermath.com/blog/ai-container-load-planning-smart-input): Where AI helps (parsing a packing list, answering questions about your plan) and where a deterministic packing engine still does the math.
- [Commercial Invoice & Packing List for Export from India](https://containermath.com/blog/commercial-invoice-packing-list-export-india): Every mandatory field on an Indian export invoice and packing list — IEC, GSTIN, 8-digit ITC-HS codes, the LUT/IGST declaration and the INR exchange rate — and why documents bounce at customs or the bank.
- [3D Container Loading Calculator](https://containermath.com/blog/3d-container-loading-calculator): What a 3D calculator computes that volume division can't — placement coordinates, orientation and stacking limits — why its answer is 10–25% lower, and how to read the plan.
- [Air Cargo ULD Load Planning](https://containermath.com/blog/air-cargo-uld-load-planning): Building up a Unit Load Device — fuselage contour limits, why ULD weight is quoted gross of tare, the 6,000 cm³/kg volumetric divisor, and why aircraft weight and balance is a separate job.
- [Container Stuffing: Process, Plan and Paperwork](https://containermath.com/blog/container-stuffing-guide): Factory vs CFS stuffing, the stuffing plan, load sequence for multi-drop, weight distribution, securing, and the SOLAS Verified Gross Mass you must declare.
- [Truck Load Planning](https://containermath.com/blog/truck-load-planning): Why a trailer under its payload limit still fails a weighbridge — axle-group limits, where the centre of gravity belongs, last-in-first-out drop order, and what load-planning software must compute.
- [Reefer Container Weight and Capacity](https://containermath.com/blog/reefer-container-weight-and-capacity): Tare, max gross and payload for 20ft and 40ft reefers, why they carry more weight but less space than a dry box, the 433 kg/m³ break-even, and genset weight on the road leg.
- [How Many Pallets Fit on a Truck?](https://containermath.com/blog/how-many-pallets-fit-on-a-truck): Floor-loaded counts for 53ft and 48ft vans, 13.6 m curtainsiders, rigids, flatbeds and step-decks — with the payload-per-pallet figures that show why weight binds first.
- [How Many Pipes Fit in a Shipping Container?](https://containermath.com/blog/how-many-pipes-fit-in-a-container): Nested vs square pipe counts for 20ft, 40ft and 40ft high cube containers from 110 to 630 mm, why steel pipe weighs out first, cut lengths, telescoping and securing.

## Comparisons

- [How ContainerMath compares](https://containermath.com/alternatives): Hub for honest, side-by-side comparisons with EasyCargo, Cargo-Planner, Cube-IQ, CubeMaster, CargoWiz, Goodloading and the SeaRates Load Calculator — including when each competitor is the better pick.
- [ContainerMath vs EasyCargo](https://containermath.com/compare/easycargo): Flat workspace pricing + AI import + carton-level packing vs EasyCargo's per-seat pricing and day tickets.
- [ContainerMath vs Cargo-Planner](https://containermath.com/compare/cargo-planner): Under half the subscription entry price ($39.99/mo vs ~$99/mo) with bundled compliance checks; Cargo-Planner stays stronger for over-gauge equipment and its embeddable 3D SDK.
- [ContainerMath vs Cube-IQ](https://containermath.com/compare/cube-iq): Transparent $39.99–$129/mo self-serve pricing vs Cube-IQ's quote-only enterprise motion; Cube-IQ wins deep WMS/TMS embedding.
- [ContainerMath vs CubeMaster](https://containermath.com/compare/cubemaster): The carton-to-container chain in one modern web tool vs CubeMaster's deep palletizing-pattern control and desktop licences.
- [ContainerMath vs CargoWiz](https://containermath.com/compare/cargowiz): Browser-based, subscription, with weight, axle and hazmat checks vs CargoWiz's one-time Windows licence and drag-and-drop editor.
- [ContainerMath vs Goodloading](https://containermath.com/compare/goodloading): Flat workspace price with AI import and carton-level packing vs Goodloading's per-user PRO subscription and its always-free demo.
- [ContainerMath vs SeaRates Load Calculator](https://containermath.com/compare/searates): A dedicated planner with saved plans, compliance checks and an API vs the freight marketplace's built-in stuffing tool and its free daily calculations.

## Case studies & use-case guides

- [Case studies index](https://containermath.com/case-studies): Customer stories and industry use-case guides — manufacturing, freight forwarding, furniture, F&B, e-commerce carton right-sizing, project-cargo flatbeds, dangerous-goods segregation, export documentation, and API/team integration.
- [From 4 Days in Excel to Minutes: a National Manufacturer](https://containermath.com/case-studies/from-4-days-in-excel-to-minutes-national-manufacturer): A manufacturer replaced a 4-day spreadsheet load-planning process with ContainerMath — minutes per shipment, ~20% better container utilisation, no rework.
- [Same-Day Container-Space Quotes for Freight Forwarders & 3PLs](https://containermath.com/case-studies/freight-forwarder-accurate-container-space-quotes): How forwarders quote how much fits a 20ft/40ft the same day — a shared box library of client SKUs, a confirmed 3D fit before quoting, and pricing space- vs weight-limited loads.
- [Loading Bulky Furniture into Export Containers](https://containermath.com/case-studies/furniture-exporter-loading-bulky-irregular-cargo): Modelling mixed flat-pack and assembled furniture in 3D before stuffing to use the full 40ft High Cube height (~18% more per container) and avoid a second container.
- [Weight-Limited Palletized F&B Loads](https://containermath.com/case-studies/food-beverage-exporter-weight-limited-pallet-loads): Planning dense canned/bottled cargo to the payload limit, not the walls — automatic pallet patterns and a balanced, road-legal load kept under weight.
- [From Container Plan to Filing-Ready Export Documents](https://containermath.com/case-studies/indian-exporter-container-plan-to-filing-ready-documents): How Indian exporters turn the cargo list built to plan the container into a Commercial Invoice, Packing List, Proforma and Invoice-cum-Packing-List without re-keying the shipment, catching missing mandatory fields before filing.
- [Right-Sizing Shipping Cartons to Cut Dimensional-Weight Costs](https://containermath.com/case-studies/ecommerce-brand-right-sizing-shipping-cartons): How e-commerce and D2C brands pick carton sizes that fit the product rather than the shelf, cutting dimensional-weight charges and void fill.
- [Loading Heavy Machinery and Out-of-Gauge Cargo onto Flatbeds](https://containermath.com/case-studies/machinery-exporter-flatbed-out-of-gauge-cargo): Planning oversized, over-height and over-width project cargo onto flatbeds and step-decks, with securing and centre-of-gravity checks before the load leaves.
- [Keeping Incompatible Dangerous Goods Apart in Every Container](https://containermath.com/case-studies/chemical-distributor-dangerous-goods-segregation): How chemical and DG distributors enforce IMDG segregation rules automatically so incompatible hazard classes are never planned into the same container.
- [Load Planning Inside Your Own ERP and TMS](https://containermath.com/case-studies/distributor-load-planning-api-shared-team-workspace): How distributors and 3PL tech teams call the load-planning engine from their own systems via the REST API and share one team workspace.

## Product & pricing

- [Container Loading (Freight)](https://containermath.com/container-loading): 3D freight load planning across 50+ vessels with payload, centre-of-gravity and per-axle checks.
- [Carton Fit](https://containermath.com/carton-fit): How many retail units fit in each shipper carton, with an exportable 3D/2D layout.
- [Export Documents](https://containermath.com/export-documents): Compliant export paperwork for 9 jurisdictions (India, EU, US, UK, UAE, Singapore, Australia, Canada + generic international) — Commercial Invoice, Packing List, Proforma, Invoice-cum-Packing-List and Shipping Instructions / Draft B/L — generated from a load plan's items with a live per-jurisdiction compliance checklist (IEC & GSTIN, EORI & VAT, EIN, HS-code depth, LUT, EEI/AES).
- [Pricing](https://containermath.com/pricing): Free trial (no card); a one-time 7-day pass at $9.99 (everything in Pro Plus for a week, one per customer per year); Starter $39.99/mo; Pro Plus $129/mo; Custom on request. Every paid plan includes both Carton Fit and freight stuffing.
- [Developer API](https://containermath.com/developer-api): Public REST API reference (cm_live_ keys) to call the packing engine from an ERP, TMS or CRM — authentication, endpoints, request/response fields, errors and per-plan quotas.
- [Embeddable Widget](https://containermath.com/embed-widget): A white-label 3D container calculator any site can embed with two lines of HTML — domain-locked publishable keys, custom theming, metered on the owner's plan (Pro Plus/Custom).