AMR Calculations

How to Calculate AMR and AGV Fleet Size, Utilization, and Payback

Work through the core intralogistics automation formulas: cycle time, fleet size, utilization, battery duty cycle, and payback period, each with real inputs and worked numbers.

Start with the pickup and dropoff cycle time, because every fleet-size number depends on it. Cycle time equals travel time plus queue plus load plus unload. Travel time is path distance divided by effective speed. An AMR covering a 180 meter round trip at an effective 0.9 m/s (after slowdowns at intersections) needs 200 seconds. Add 15 s pickup, 15 s dropoff, and 20 s average queue and you get 250 s per move, or 14.4 moves per hour per robot. Use the Pickup and Dropoff Cycle Time Calculator to layer in door delays and elevator waits, which routinely add 30 to 60 seconds each.

Fleet size follows directly. Required robots equals demand moves per hour divided by moves per hour per robot, divided by planned availability. If the plant needs 260 moves per hour, each robot delivers 14.4, and availability runs 0.85 (charging and faults), then 260 / 14.4 / 0.85 = 21.2, so you round up to 22 units. The AGV Fleet Size Capacity Calculator does this rounding plus a peak-hour surge factor. Never size to the average hour: a 1.3 peak-to-average ratio on that line means you actually design for 338 moves per hour, pushing the fleet to 28.

Utilization tells you whether that fleet is right-sized. AMR utilization equals productive time divided by scheduled available time. Productive time is moves per shift times cycle time. If 22 robots run an 8 hour shift (28,800 s each) and complete 2,600 moves at 250 s each, productive time is 650,000 s against 633,600 s scheduled, which flags overload above 100 percent. The AMR Utilization Calculator separates travel, idle, and charging so you can see whether idle sits in a healthy 15 to 25 percent band or whether you are starved for work.

Battery duty cycle decides how many robots you actually keep on the floor. Runtime equals usable capacity divided by average draw. A 48 V, 40 Ah pack holds 1.92 kWh; at 80 percent usable that is 1.54 kWh. If the robot averages 350 W moving and idling, runtime is 1.54 / 0.35 = 4.4 hours. Charge time at a 0.5C rate is roughly 2 hours to 80 percent. The AMR Battery Charge Capacity Calculator converts this into a duty ratio: 4.4 run to 2.0 charge means about 31 percent of the fleet is off-floor at any moment if charging is not staggered.

Tugger routes use a different unit: carts and stops, not single moves. Route capacity equals loop time divided into the shift, times carts per train. A milk-run loop of 12 minutes with a 4 cart train running a 480 minute shift yields 40 loops, so 160 cart-deliveries per shift. The Tugger Route Capacity Calculator lets you test whether adding a fifth cart (raising delivery 25 percent) still fits inside your takt, since dwell at each of 8 stops at 45 seconds already consumes 6 minutes of the 12 minute loop.

Payback ties the physical numbers to a period, not a price. Payback in years equals installed system cost divided by annual labor and handling savings. If a 3 robot cell displaces 2.5 full-time equivalents at a fully loaded 62,000 dollars each, annual savings are 155,000 dollars; a 380,000 dollar install pays back in 2.45 years. The AMR ROI Calculator and Autonomous Forklift Payback Calculator handle this, and the Internal Logistics Labor Savings Calculator isolates the labor term so you are not double-counting maintenance in both cost and savings.

Congestion quietly breaks all of the above, so quantify it before trusting your effective speed. A route congestion score weights intersection conflicts, aisle width, and traffic density. When two-way traffic shares a 1.6 meter aisle, effective speed can drop from 1.2 m/s to 0.7 m/s, a 42 percent hit that inflates cycle time from 250 s to roughly 330 s and quietly demands 30 percent more robots. Run the Route Congestion Score Calculator early; a score in the high band tells you to fix layout before buying units, since a wider aisle is far cheaper than four extra AMRs.

Tie the chain together with a single move-throughput sanity check. Multiply fleet size by moves per hour per robot by availability and confirm it clears peak demand with 10 to 15 percent headroom. In the running example, 22 robots times 14.4 times 0.85 equals 269 moves per hour against a 260 average but a 338 peak, so 22 units are short and 28 is correct. Recompute cycle time whenever payload, path, or charging strategy changes, because a single input like a new elevator wait cascades through fleet size, utilization, and payback all at once.

Published 2026-07-01.