Maths and geometry calculators

Questions these calculators answer

How do you calculate the volume of a cylinder?

Multiply pi by the radius squared, then by the height: V = πr²h. If you measured the diameter instead, halve it first. Working in metres gives cubic metres, and one cubic metre is exactly 1,000 litres — so a cylinder half a metre across and one metre tall holds about 196 litres.

How do you calculate slope?

Divide the rise by the run. That fraction is the slope: multiply it by 100 for a percentage grade, take its arctangent for the angle in degrees, or invert it for a 1-in-X ratio. A 150 mm fall over 3 metres is 0.05 — a 5% grade, 2.86 degrees, and a 1-in-20 slope.

How do you simplify a surd?

Find the largest perfect square that divides the number under the root, split the surd into that square times the remainder, then take the square root of the perfect square outside. For √72 the largest square factor is 36, so √72 = √36 × √2 = 6√2.

How is pi calculated?

By series that converge on it. Machin's formula, π = 16·arctan(1/5) − 4·arctan(1/239), has been the practical choice since 1706 because both arctangent series converge quickly. Each term of the 1/5 series adds about 1.4 decimal places, so a few hundred terms gives hundreds of digits.

How do I work out my exact age?

Subtract the date of birth from today's date, borrowing days from the previous month when needed. Someone born on 15 March 1990 is 36 years, 7 months and 12 days old on 27 October 2026, which is 13,375 days. They reach Age Pension age (67) on 15 March 2057.

How many days are there between two dates?

Subtract the earlier date from the later one. From 1 July 2026 to 30 June 2027, the span of a financial year (1 July to 30 June), is 364 days, or 365 days if the last day is counted. That is 52 weeks and 0 days, or 0 years, 11 months and 29 days.

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. 10% of 250 is 0.10 x 250 = 25. To add GST at 10%, multiply by 1.1; to take it out of a total, divide by 1.1. So 110 including GST is 100 before GST.

How do I split a bill between friends?

Add any surcharge and tip to the bill, then divide by the number of people. A $186.00 bill for 4 people is $46.50 each. With a 10% tip it is $51.15 each. Tipping is optional in Australia, and service is not added by default.

How many stone and pounds is 80 kg?

Divide the kilograms by 0.45359237 to get pounds, then divide by 14 for stone. 80 kg is 176.4 pounds, which is 12 stone 8.4 pounds. To go the other way, multiply pounds by 0.45359237; one stone is 14 pounds or about 6.35 kilograms.

How many feet and inches is 175 cm?

Divide centimetres by 2.54 to get inches, then divide by 12 for feet. 175 cm is 68.9 inches, which is 5 feet 8.9 inches. To go the other way, multiply total inches by 2.54. One foot is exactly 30.48 centimetres.