Why half an ounce matters
The force a rotating imbalance makes is the mass times the radius times the square of the angular speed. Put half an ounce five inches from the spindle centre at 3,000 rpm and the arithmetic gives 39.9 pounds of force, or 178 newtons, going round 50 times a second. Half an ounce is roughly the weight of a tablespoon of water. Nobody would guess it was worth forty pounds.
The reason it is so large is the square on the speed. At 3,000 rpm the angular speed is 314 radians a second and the square of that is 98,700, which is the factor doing all the work. Everything about balancing a blade follows from that one exponent.
The square law, read backwards
Halve the speed and the force falls to a quarter. The same half ounce at 1,500 rpm is 10 pounds instead of 40, and at 1,200 rpm it is 6.4. That is why an unbalanced blade can feel almost civilised at idle and shake the machine apart at full throttle, and it is why comparing a vibration at two different engine speeds tells you more than feeling it at one.
It also means small changes in deck speed matter more than they look. Going from 3,000 to 3,300 rpm — ten percent — raises the same imbalance force by twenty-one percent.
Radius is the guess in the middle
Mass and speed can both be measured. Where the surplus metal actually sits cannot, and the answer scales in a straight line with it, so a radius that is twice as far out gives a force twice as large. Grinding removes metal from the outer part of the cutting edge, which puts the difference well out towards the tip rather than near the middle, and five inches on a 21 in blade is a reasonable place to start. If you want a bound rather than a figure, run it at the tip radius and at half of it and read the range.
What a balancer can and cannot see
A cone, a nail or a magnetic balancer finds static imbalance: with the blade free to turn about its centre, the heavy end goes to the bottom. That is the quantity this page works with, and getting it close is worth doing every time a blade comes off the grinder.
What none of them see is a blade that is bent out of plane, twisted along its length, or has one lift wing damaged. Those produce a couple rather than a simple out-of-balance force, and they shake a deck with the blade balancing perfectly on the cone. If a blade balances and the machine still buzzes at once per revolution, the balance is not the fault — and the spindle itself, the pulley and the blade adapter are all in the same rotating assembly and all capable of the same thing.
Three blades, three phases
The number the page prints is for one blade. A wide deck has three, each with its own imbalance pointing in its own direction, and they do not cancel — they add and subtract in a pattern that changes every instant because the spindles are not synchronised. The load ends up in the spindle housings, the deck shell, the belt and the machine frame, and on a walk-behind the last stop is the handles, which is why an out-of-balance blade is something you feel through your hands before you see it in the cut.
Questions people ask
How much force does an unbalanced mower blade make?
Half an ounce sitting five inches from the spindle at 3,000 rpm works out at about 40 pounds of force, rotating fifty times a second. The formula is mass times radius times the square of angular speed, and the square is what makes such a small weight difference produce such a large number.
Why does an unbalanced blade shake worse at full throttle?
Because the force goes with the square of the speed. The same imbalance that pulls 10 pounds at 1,500 rpm pulls 40 at 3,000. Doubling the speed quadruples the force, which is why a blade that feels acceptable at idle can be violent at cutting speed, and why comparing the shake at two speeds tells you more than feeling it at one.
Do I need to balance a mower blade after sharpening?
Grinding removes metal, and it rarely removes exactly the same amount from both ends, so a sharpened blade is out of balance unless it is checked. Whether the residual amount matters is a question for your spindle and your blade maker rather than for this page, which supplies no threshold and simply converts a weight difference into the force it makes.
My blade balances on a cone but the mower still vibrates. Why?
A cone finds static imbalance only, meaning which end is heavier. It cannot see a blade bent out of plane, twisted along its length, or with one lift wing damaged, and all three shake a deck while balancing perfectly. The spindle, pulley and blade adapter are part of the same rotating assembly and can do the same thing.
What radius should I use for the imbalance?
Where the surplus metal actually sits, which for a grinding difference is out towards the tip rather than near the middle. The force scales straight in line with it, so doubling the radius doubles the answer. If you cannot pin it down, run the page at the tip radius and at half of it and treat the two answers as the bounds.