Mental Math for Pilots – Timed Rule-of-Thumb Drills

How it works

Mental math for pilots: each drill is a rule of thumb or basic calculation from Federal Aviation Administration handbooks, such as 3 miles per 1,000 feet. Rules of thumb are approximations; this is arithmetic practice, not flight planning or training.

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What each question stands for

Questions show as bare arithmetic. In Headings, 125 + 180 is a reciprocal. In Speed, time and distance, 540 ÷ 60 turns knots into miles a minute. In Turns, 270 ÷ 3 is the seconds for a standard-rate turn, and 15% of 120 is a bank angle.

Descent and fuel

Descent has two rules of thumb for miles out, 25 × 3 and 6,000 ÷ 300, and groundspeed times 5 for feet a minute on a 3 degree path. Fuel has gallons an hour times hours, and gallons times 6 for pounds of gasoline.

The Drill menu is under More options; the list lower down names the rule behind each drill.

Questions and answers

What mental math do pilots use?

The handbooks drilled here use a few small calculations: add or take away 180 for a reciprocal heading, divide groundspeed by 60 for miles a minute, multiply thousands of feet by 3 for a descent, and multiply gallons by 6 for pounds of gasoline.

What is the 3 to 1 rule?

A rule of thumb for descent planning that the Instrument Procedures Handbook gives for jets: 3 nautical miles for each 1,000 feet to lose. Its example is 25,000 feet, which is 25 × 3 = 75 miles.

How do you work out a reciprocal heading in your head?

Add 180 to a heading under 180, and take 180 from one over it. The Instrument Flying Handbook does it in round numbers: for 305, take away 200 and add 20, which gives 125.

Is this a pilot aptitude test?

No. It is an unverified self-test of arithmetic. It is not the test of any airline, school or agency, it has no passing score, and a score here counts toward nothing.

All 12 drills

Headings 2

Reciprocal: add 180 The opposite direction is 180 degrees away. A handbook shortcut for a heading under 180: add 200, take away 20, so 125 becomes 325, then 305.
Reciprocal: take away 180 For a heading over 180 the shortcut runs the other way: take away 200 and add 20, so 305 becomes 105, then 125.

Speed, time and distance 2

Knots to miles a minute Groundspeed in knots divided by 60 is nautical miles a minute: 120 knots is 2, and 180 knots is 3.
Miles a minute times minutes Miles a minute times the minutes flown is the distance: 10 minutes at 2 miles a minute covers 20 nautical miles.

Turns 2

Bank angle: 15% of airspeed A handbook rule of thumb for the bank of a standard-rate turn: 15 percent of true airspeed. Divide by 10 and add half of that: 120 knots gives 12 + 6 = 18 degrees.
Seconds for a standard-rate turn A standard-rate turn is 3 degrees a second, so the heading change divided by 3 is the time in seconds: 120 degrees takes 40.

Show all 12 drills (6 more)

Descent 3

Feet a minute: groundspeed times 5 On a 3 degree path the rate of descent in feet a minute is about the groundspeed times 5: 120 knots gives 600.
Miles out: feet to lose divided by 300 A second handbook rule of thumb: feet to lose divided by 300. From 7,000 feet down to 1,000 is 6,000 ÷ 300 = 20 miles.
Miles out: thousands of feet times 3 The 3 to 1 rule a handbook gives for jets: 3 nautical miles for each 1,000 feet to lose. For 25 thousand feet that is 25 × 3 = 75 miles.

Fuel 2

Gallons an hour times hours Fuel for a flight is the rate of use times the time: 5 gallons an hour for 4 hours is 20 gallons.
Gallons of gasoline to pounds The handbook standard weight for gasoline is 6 pounds a US gallon, so 30 gallons weigh 180 pounds.

Mixed 1

Mixed cockpit math Eight of the drills in one run: reciprocals, miles a minute, turn time, bank angle and the times 3, 5 and 6 drills.

How this list was compiled: Drills and notes written for this page in October 2026. Each drill is one rule of thumb or basic calculation printed in a handbook of the Federal Aviation Administration, read at faa.gov on 2 October 2026. Instrument Procedures Handbook (FAA-H-8083-16B), Chapter 3, Descent Planning: 3 nautical miles for each 1,000 feet to lose, with 25,000 feet as 75 miles; the altitude to lose divided by 300; groundspeed times 5 as the rate of descent on a three-degree path; 120 knots as 2 nautical miles a minute (https://www.faa.gov/sites/faa.gov/files/regulations_policies/handbooks_manuals/aviation/instrument_procedures_handbook/FAA-H-8083-16B_Chapter_3.pdf). Instrument Flying Handbook (FAA-H-8083-15B), Chapter 7: a standard-rate turn of 3 degrees a second and the heading change divided by 3; 15 percent of true airspeed as the approximate bank angle, with 120 knots as 18 degrees; the reciprocal of 305 worked as take away 200, add 20 (https://www.faa.gov/sites/faa.gov/files/regulations_policies/handbooks_manuals/aviation/FAA-H-8083-15B.pdf). Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), Chapter 10: gasoline at 6 pounds a US gallon (https://www.faa.gov/sites/faa.gov/files/12_phak_ch10.pdf); Chapter 16: fuel as flight time multiplied by the rate of consumption, distance as miles a minute multiplied by minutes, and a course of 065 with its reciprocal 245 (https://www.faa.gov/sites/faa.gov/files/18_phak_ch16.pdf). Questions are generated in the browser from the number ranges stored with each drill and every answer is computed at that moment. The rules of thumb are approximations. This page is arithmetic practice, not flight planning and not flight training. Licence: own work; the rules of thumb are from handbooks of the Federal Aviation Administration, United States government works in the public domain