Load chart math without a calculator for the Core exam

The Core handbook lists its own arithmetic task inside the Load Charts domain (task 4.2), and the Core study guide suggests setting aside about a fifth of your chart time for pencil-and-paper practice. All the numbers below are invented for teaching. They are not from any manufacturer's chart or any exam.

The five operations behind every chart problem

1. Subtracting deductions from gross capacity to reach net capacity.
2. Adding up deductions first: hook block, jib, rigging.
3. Multiplying for load moment or for geometry like radius.
4. Percentages, such as how much of the net capacity a load uses.
5. Choosing a row when your radius or boom length falls between listed entries.

If you can do those five without hesitation, the chart workflow stops feeling heavy. The how to read a crane load chart guide covers the lookup order; this page covers the arithmetic after you have the right cell.

Three paper habits that prevent most errors

Write the units on every line. "24,000" is a bad note. "24,000 lb gross" is a good one. Unlabeled numbers are how a radius ends up inside a weight calculation.

Add the deductions first, then subtract once. Subtracting three items one at a time gives you three chances to slip. Total them, check the total, then take it from gross.

Sanity-check against the gross. Net capacity must be smaller than gross. A net that is bigger, or suspiciously close to zero, means you made a slip. This takes five seconds and catches most mistakes.

Three worked examples on invented numbers

1. Gross to net

An invented chart gives a gross capacity of 18,500 lb at your radius. The notes list a 700 lb hook block, a 900 lb stowed jib and 350 lb of rigging.

• Deductions: 700 + 900 = 1,600, then 1,600 + 350 = 1,950 lb.
• Net: 18,500 − 1,950 = 16,550 lb.
• Check: 16,550 is less than 18,500. Good.

A faster way to subtract 1,950: take away 2,000, then give back 50. 18,500 − 2,000 = 16,500, plus 50 = 16,550. Rounding to a friendly number and correcting is the main mental shortcut worth learning.

2. Percentage of capacity

Say a 12,000 lb load is planned against a net capacity of 16,000 lb. What share is that?

12,000 ÷ 16,000 simplifies to 3 ÷ 4, which is 75%. Simplify first by dropping matching zeros and then dividing by common factors. For awkward ratios, estimate with benchmarks: 10% of 16,000 is 1,600, and 12,000 is 7.5 of those chunks, so 75%.

3. Radius by hand

A 50 ft boom is set at a 60 degree angle. Radius, ignoring boom-foot offset and deflection, is boom length times the cosine of the angle. The cosine of 60 degrees is 0.5, a value worth memorizing, so the radius is 50 × 0.5 = 25 ft. A boom at 0 degrees would have a radius equal to its length, and one at 90 degrees would have none. Those two end points catch most wrong answers before you finish. The crane radius and boom angle calculator lets you check this on other angles after you have done it by hand.

When your number falls between two rows

Take an invented chart that lists 4,000 lb at 20 ft and 3,200 lb at 25 ft, and your radius is 22 ft. Chart notes decide what you may do: some allow a straight-line value between rows, others tell you to use the next longer radius. Read the notes first. Then:

• Next longer radius: use 3,200 lb. No arithmetic needed.
• Straight-line value: the drop across 5 ft is 800 lb. You are 2 ft in, which is 2 ÷ 5 of the way, so 4,000 − (2 ÷ 5 × 800) = 4,000 − 320 = 3,680 lb.

The common error is applying the method your notes do not allow. Lookup rule first, math second.

After each worked example, redo it with different numbers before you move on. Copying a method you just watched proves little. Changing the inputs and getting the right answer by yourself shows the method is yours. Keep the first attempt on paper, in pencil, with units on every line, exactly as you would in the exam room.

A five-minute daily drill

Set a timer and do this every day for two weeks:

1. Write five invented gross capacities and three deductions each.
2. Total the deductions, then subtract.
3. For two of them, compute the percentage used by a load you pick.
4. Mark each answer, then check them with the net capacity calculator only after you have finished by hand.

If you also want to practice weight estimates by hand, work a plate or pipe by volume times density and check it with the load weight calculator afterward. Track how long it takes. Speed comes within a week. Once the arithmetic is automatic, chart problems on the load chart practice tool go faster because you only have to think about the lookup. When you want to check a whole lift, the crane percent of capacity calculator turns a chart number, a load and the deductions into one percent.

Once the arithmetic is steady, range diagrams and working-area charts covers the lookup half of the problem.

The free 10-question check includes chart items, so it shows exactly which areas to study first, and whether hand math or chart lookups is your weaker side.

FAQ

Is a calculator allowed on the Core written exam?

No. The current handbook lists the Core as 95 questions in 90 minutes with no calculator permitted, so every subtraction and multiplication is on paper or in your head.

Is a calculator allowed on the specialty exams?

The LAT, TLL and TSS specialty exams allow one, but Service Truck Crane (STC) does not. The rule differs by exam, so see the specialty written exams comparison before you plan.

How do I get faster at mental math?

Round to friendly numbers and correct afterward, as in the 2,000-minus-50 trick above. Add deductions in a fixed order, and keep the daily five-minute drill going. Speed improves with repetition far more than with theory.

What do I do when a number falls between two chart rows?

Check the chart's notes for how to handle in-between values, then apply only that method. If the notes allow a straight-line value, work it out proportionally. If they say to use the next listed value, take that and move on.