Most changes to Earth's surface are too slow to see: a river deepens its canyon by a fraction of a millimeter a year. But a fraction of a millimeter, repeated for millions of years, adds up to a canyon. It is a rate problem: total change = rate × time. A few erosion events, like landslides, happen in minutes.
Key idea
Total change = rate × time. Tiny yearly changes, kept up for millions of years, build canyons and wear down mountains; a few events, like landslides, floods and eruptions, change the land in minutes or days.
Why it works
Deep time is hard to picture because our lives are so short. If a river cuts down 0.3 mm a year, you would never notice it in a lifetime: about 2.5 cm in 80 years. But 6 million years is 75,000 lifetimes. Multiply: $0.3 \times 6{,}000{,}000 = 1{,}800{,}000$ mm, which is 1,800 m, about as deep as the Grand Canyon.
Worked example: Unit by unit
A mountain range wears down by about 0.05 mm a year. How much lower is it after 10 million years, in meters?
- $0.05 \times 10{,}000{,}000 = 500{,}000$ mm.
- 1,000 mm = 1 m, so $500{,}000 \div 1{,}000 = 500$ m.
Answer: 500 m
Worked example: How long?
A river cuts a 600 m deep canyon at about 0.2 mm a year. About how long did that take?
- Change to millimeters: $600 \times 1{,}000 = 600{,}000$ mm.
- Time = depth ÷ rate: $600{,}000 \div 0.2 = 3{,}000{,}000$ years.
Answer: About 3 million years
Common mistake
Thinking big landforms like canyons must come from one sudden event, because tiny yearly changes are hard to picture adding up. Check by multiplying the rate by the time: small rates over millions of years give hundreds or thousands of meters. Fast events do happen too, but they reshape a slope or a valley floor, not a whole canyon.